Teaching Maths

aSGuest873

Download

Post to :

URL :

Related Presentations :

Add to Flag Embed

Views: 41

Category: Education

Presentation Description

No description available.

Comments

Presentation Transcript

Teaching Maths-Phobic Undergraduates :

Teaching Maths-Phobic Undergraduates Teaching Maths & Quantitative Skills at Lancaster 28th March 2007

Problem Statement: :

Problem Statement: Quantitative Skills (QS) are core requirements of many degree schemes (and crucial graduate/life/career skills) Many UG students on these schemes view quantitative material as: Repulsive Boring Fearful Irrelevant to their interests

Aspirations: :

Aspirations: Graduates who: Have got over their repulsion etc. towards QS Appreciate the value of quantitative techniques in their discipline Can understand and explain quantitative techniques and their outcomes Can use these techniques appropriately and make accurate assessments of the meaning of their outcomes

The Tasks at Hand: :

The Tasks at Hand: Getting the course design right Breaking down the barriers Making it relevant & valuable Getting their mindset & knowledge right Getting them up-skilled and practised

0. Starting Points: :

0. Starting Points: Like your students Like your material DON’T THINK: “My students are idiots/lazy” “My material is boring”

0. Starting Point: :

0. Starting Point: It’s not about you, it’s about them c.f. climbing mountains, learning to swim It’s not “teaching”, it’s “facilitating learning” Whole class modules should be “socialist” Higher end, optional modules can be “elitist” Discuss…

1. Getting the Course Design Right: :

1. Getting the Course Design Right: Get the Context Straight: Quantitative skills often taught in a “bolt-on” module Quantitative material “embedded” throughout syllabus Need to get this all aligned before settling on content & degree of coverage required in both QS modules and those that use QS

1. Getting the Course Design Right: :

1. Getting the Course Design Right: Challenge the Tradition: Often, “received” content of QS modules has been conditioned by anachronistic guiding principles, so ask, for example: Do students really need to learn to write their own Fortran programs – or would e.g. developing skills in software use be more valuable? Should frequentist inferential statistics be the sole focus of QS modules, or are there other things that would be equally, or more, relevant and useful?

2. Breaking down the Barriers :

2. Breaking down the Barriers You will be assigned x contact hours and y students (x << y) Use the contact hours wisely, they are very precious! Whole class sessions (lectures) are for getting your message across: breaking down barriers, making friends, opening doors, lighting fires etc. Practical sessions are for the students to practice “walking the walk”

Slide 10:

GEOG 119 Basic Skills for Geographical Research Lectures 5-11 Quantitative Skills Dr. Andrew Folkard a.folkard@lancaster.ac.uk

Descriptive Statistics :

Descriptive Statistics Mean Variance Skewness Kurtosis

Why do we need quantitative skills? :

Why do we need quantitative skills? What sort of problems can we solve with quantitative approaches, and what can’t we solve in this way?

GEOG 201: Geographical Techniques :

GEOG 201: Geographical Techniques Lecture 5: How to use Regression and Correlation

Lake Baikal :

Lake Baikal Aldar Gorbunov and Sergei Marchenko

Lake Baikal :

Lake Baikal Todd, MC, and Mackay, AW, 2003, Large-Scale Climatic Controls on Lake Baikal Ice Cover, Journal of Climate, 16, 3186-3199 Available here: http://geog-info.lancs.ac.uk/courses/geog201/baikal.pdf Use long-term records (1869-1996) of winter ice duration formation date breakup dates analyzed to determine temporal trends Decreaseing ice duration, thickness Later formation, earlier breakup relationship with large-scale atmospheric circulation Variability in ice related to winter temperatures over a wide area Thus, ice cover a robust indicator of continental-scale winter climate Deduce atmospheric processes responsible

Slide 17:

Hello Everybody!!

Lake Baikal :

Slide 19:

Want to have some fun?

Lake Baikal :

Slide 21:

Everybody shout “Broccoli!” when you see the picture of some broccoli…

Lake Baikal :

Slide 23:

Ready?

Lake Baikal :

Slide 25:

1…

Lake Baikal :

Slide 27:

2…

Lake Baikal :

Slide 29:

3…

Lake Baikal :

Lake Baikal Todd, MC, and Mackay, AW, 2003, Large-Scale Climatic Controls on Lake Baikal Ice Cover, Journal of Climate, 16, 3186-3199 Available here: http://geog-info.lancs.ac.uk/courses/geog201/baikal.pdf Use long-term records (1869-1996) of winter ice duration formation date breakup dates analyzed to determine temporal trends Decreasing ice duration, thickness Later formation, earlier break-up relationship with large-scale atmospheric circulation Variability in ice related to winter temperatures over a wide area Thus, ice cover a robust indicator of continental-scale winter climate Deduce atmospheric processes responsible

2. Breaking down the barriers :

2. Breaking down the barriers Acting the court jester the whole time isn’t a good idea Hooking them via the subject matter may work better But I find it helps to show that you’re on their level and you don’t have to be po-faced to be intellectually rigorous Generates a reservoir of goodwill that is extremely valuable in this context

3. Making it relevant & valuable :

3. Making it relevant & valuable Could start from the maths, give the grounding, then move onto applications in… In practice, you lose them on the “m” of “maths” Need to demonstrate that there are important, interesting questions that simply can’t be answered without a quantitative approach… …so start with those questions

The Mann-Bradley-Hughes (MBH) “hockey stick” graph :

The Mann-Bradley-Hughes (MBH) “hockey stick” graph A blip or a serious change? Response to counter-argument: http://people.aapt.net.au/~johunter/greenhou/open_review.html A counter-argument: http://www.john-daly.com/hockey/hockey.htm Original paper: http://www.ncdc.noaa.gov/paleo/pubs/millennium-camera.pdf

Is Third World Aid a Good Thing? :

Is Third World Aid a Good Thing? Argument for: http://news.bbc.co.uk/1/hi/sci/tech/4210122.stm Argument against: http://news.bbc.co.uk/1/hi/sci/tech/4209956.stm

Is Third World Aid a Good Thing? :

Is Third World Aid a Good Thing? How good a relationship between Government Health Expenditure & Infant Mortality rate does there have to be to convince you that they really are linked?

Key Questions: :

Key Questions: When does a relationship start to suggest that there really is a link between things, rather than it just being a coincidence? Is this just a matter of personal opinion, or is there a more reliable, objective way of making this decision? Important questions: they determine global political policy, global scale financial & economic decisions etc.

The Need for an Objective Answer :

The Need for an Objective Answer Can’t base important decisions like these on purely subjective judgements So many intangibles, need to “objectivize” where we can Quantitative approach can save us!

3. Making it relevant & valuable :

3. Making it relevant & valuable In our subjective, democratized, “have-your-say” world… …where anti-QS propaganda is rife… …need to fight against the tide and emphasise the value of objective, quantitative skills

4. Getting their mindset & knowledge right :

4. Getting their mindset & knowledge right This is where whole class sessions start to lose their value Needs clarity and reinforcement Initially, worked examples to follow through, not problem-solving exercises Every step needs taking at the right pace (i.e. very gently) Need to engender flexibility of understanding Need to get language, meaning thoroughly correct (e.g. null hypothesis testing…)

4. Getting their mindset & knowledge right :

4. Getting their mindset & knowledge right Get your learning support properly sorted: TA’s E-learning support Practical exercises to take away Supporting notes, reading …and/or expect a lot of knocks on your door Be strict but generous with your office hours

5. Getting them upskilled & practised :

5. Getting them upskilled & practised It’s not just the technique itself… …it’s identifying where to use it… …and how to interpret the outcome in context

5. Getting them upskilled & practised :

5. Getting them upskilled & practised Best vehicle for this (and assessment) is a project (i.e. project-based learning) Needs careful attention at every step Embeds QS into research design & execution If possible, link to departmental research (i.e. research-led teaching) Useful as “dry-run” for dissertations

5. Getting them upskilled & practised :

5. Getting them upskilled & practised “State of the Campus” report What general area will your project be in? What specific hypotheses/questions will it aim to test/answer? What techniques will you use to test/answer them? What data do you need to collect, and how much of it will you need? What are the potential pitfalls and how will you get around them?

Feedback on Assessment :

Feedback on Assessment If course design has been done right, this will actually be of value! Use this an a further opportunity to get the message across

The Tasks at Hand: :

The Tasks at Hand: 0. Starting Points Getting the course design right Breaking down the barriers Making it relevant & valuable Getting their mindset & knowledge right Getting them up-skilled and practised