What Everyone is Talking AboutMath for the 21st CenturyMiroslav LovricMcMaster University

I will talk about, and comment on:

• Jobs and “job-ready” graduates

• Math is present (mostly through technology) in many aspects of our daily lives

• Our students’ attitudes and beliefs vs the image of “life long learners,” “forward-thinking leaders”

• Teaching calculus in 21st century: for all or for some?

• Service courses – opportunities missed

• New initiatives at McMaster and elsewhere

Jobs and “job-ready” graduates

Canada’s youth (15-24) unemployment rate (2014) is 13.5-14.5%Ontario youth (15-24) unemployment rate (2013) is between 16 and 17.1% = twice the overall unemployment rate

[MacLean’shttp://www.macleans.ca/work/jobs/the-myths-about-canadas-skills-gap/Canadian centre for Policy Alternativeshttps://www.policyalternatives.ca/publications/reports/young-and-jobless]

Experts say that Canada, for all its hand-wringing about the economy, does a woeful job of tracking the all-important labour market. We know very little about who is hiring, what skills they are looking for and how graduates of specific programs fare in the real world.

[http://www.macleans.ca/work/jobs/the-myths-about-canadas-skills-gap/]

Despite complaints about a shortage of skilled workers, studies show corporate spending on training has been in steady decline for the past two decades.

[http://www.macleans.ca/work/jobs/the-myths-about-canadas-skills-gap/]

So, 21st century: we have to provide content and train our students

How do we train? What skills?

[U Waterloo]

Product Manager (Interactive Video Services) at Rogers Cable (BSc Math)Senior Supply Chain Analyst, Loblaw Companies Limited (BSc Math + MBA)Software Engineer, Yahoo (BMath CS, Software Eng)Several startups (BMath in CS)Vice-President of Investments, Covington Capital Corporation (BSC Math + Accounting)Business Relationship Account Manager, BMO (BMath and CS + MBA)Actuary, Milliman Inc. (Hons Actuarial Sci)Team Lead, Research In Motion (CS)Product Designer, Desire2Learn (CS)

Research Associate, Toronto General Hospital (MSc in Math)

Research Scientist, Environment Canada (BSc Math, MSc Meteorology, PhD Atmospheric Sci)

Research Scientist, Natural Resources Canada's CanmetENERGY (MSC Math, PhD Chem Eng)

Research Scientist, National Water Research Institute at the Canada Centre for Inland Waters (PhD Stats)

Chair in the School of Industrial and Systems Engineering at Georgia Tech (PhD Combinatorics and Optimization)

Associate Professor in the Department of Applied Mathematics at the University of Waterloo (PhD Math)

At least some biased feeling:

Makes sense to combine math with something else

Financial, insurance industries (still) offer jobs

“Math jobs” do not necessary involve working with math

Computer science background is good to have

Research positions in industry, government, universities – need at least MSc

The failure of the Ministry of Training, Colleges, and Universities to address the over-supply of graduates from teachers colleges is a massive oversight failure and the current draw-down of students continues to be a policy blunder.

[http://www.youthandwork.ca/2013/01/is-teachers-college-worth-it-nope-heres.html]

“Teachers face tough entry-job hurdles in an increasingly crowded Ontario employment market”

Our government must provide accurate, reliable, comprehensive job-related information

• to colleges and universities• to general public

and must provide much better, more reliable and serious guidance in terms of future trends in the job markets

Employers should be forced to pay universities for training their future employees

“Math (in big part through technology) is everywhere in our daily lives”

• driving directions, GPS• DNA sequencing technicians• medical imaging (CT, MRI, etc.)• auto correction in spell checkers• internet traffic, data encryption, data compression• taxes and tax returns• accounting• mortgage calculators• translation between languages• investments and portfolio management, financial planning• insurance policiesetc.

Technology makes us think less; we lose certain cognitive (and other) abilities

• in many cases, humans do a little beyond supervising/ serving machines and computers (airplane pilots, GPS)

Do we need more or less math than what is presently taught?

Do we need the same math we have been teaching, or a different math?

Most people are math users, and ignorant of math.

Some people are curious and sophisticated math users.

Very small number of people actually do something with math (math experts).

Interest, motivation?

… mathematics was selected by the smallest group

“I'm happy to see that science stimulates the European youth,” commented European Science and Research Commissioner Janez Potocnik.

[…] survey shows that there is a huge reservoir of interest and support to science in the young generation. However, the low interest in engineering and scientific studies is a major concern, as well as the gender imbalance. We must reverse this trend because talented and educated 'brains' are major EU assets in the current global competition.

The Science Learning Centre in London, UK, surveyed 11,000 students aged 11-15 for their views of science and scientists

around 80% of pupils thought scientists did "very important work" 70% thought they worked "creatively and imaginatively”

around 40% said they agreed that scientists did "boring and repetitive work”around 70% said they did not picture scientists as "normal young and attractive men and women”

[BBC News [no author mentioned] (2006). Science ‘not for normal people.’ Available at: http://news.bbc.co.uk/2/hi/uk_news/education/4630808.stm]

very few plan to become scientists; reasons included

”because you would constantly be depressed and tired and not have time for family"

"because they all wear big glasses and white coats and I am female"

Average student in Canada spends about 14 hours a week studying, down from 24 hours several decades ago.

(Similar stats for other countries)

[New Report Shows Students Are Studying Less But Getting Better Grades http://www.edudemic.com/new-report-shows-students-studying-less-getting-better-grades/

The decline of studying http://www.macleans.ca/news/canada/the-decline-of-studying/

Is college too easy? As study time falls, debate riseshttp://www.washingtonpost.com/local/education/is-college-too-easy-as-study-time-falls-debate-rises/2012/05/21/gIQAp7uUgU_story.htm]

‘Only about 11 percent of full-time students say they spend more than 25 hours per week preparing for their classes - the amount of time that faculty members say is necessary to succeed.’

[National Survey of Student Engagement: http:/nsse.iub.edu

Hoover, E. (2004) Undergraduates Study Much Less Than Professors Expect The Chronicle of Higher Education, November 15, 2004]

Are we interested in “long-life learning”?

We need to know better who our students are, what motivates them, what are their beliefs about math (and education in general)

We need to abandon romantic views and political correctness about education and decide: do we teach some math to all students, and/or do we teach more math to some students and less to other?

What math (and how much of it) will prepare our students for global competition for STEM jobs?

Present situation:

We teach • math for “specialists” • math for “others” (service courses)• remedial math courses

Service (and remedial) courses:

• many students are weak not only in abstract thinking, logical thinking, but also in interpretation and communication of math ideas; they have very few, if any, ideas about proof

We teach calculus and possibly linear algebra and often do not go beyond routines and things which are “easy” to learn

Most students who take these courses, and no other math courses, will not learn much and will never use that math.

Nor they intended to from the start.

Inevitable questions:

Why do we teach calculus to students who need one course/ one credit in math?

Why do we insist on teaching calculus in high school?

What’s so special about calculus that it dominates math curricula?

After decades of unsuccessful attempts at “fixing” teaching calculus, why are we still trying to “fix” it?

Suggestions:

• Stop teaching calculus they way it has been taught for decades

• Teach a different (different from present) calculus to math and stats majors

• Teach appropriately designed calculus to selected other majors.

Why calculus? Because we can get farthest with it (e.g. math modelling in life sciences)

• Remaining students – teach relevant math or don’t teach math at all

As well …

• No need for calculus in high school (what do students actually learn about calculus?)

Instead, bring back geometry, and teach in new ways (for instance, using software)

• Make math optional after grade 10 in high school and at the same time make vocational education lot more attractive, meaningful and useful to young people

Changing attitudes toward vocational education

Why don’t we make students happy, instead of scarring them forever!

Skills that math can teach them can be gained in other courses.

Brain of a person experiencing physical pain

Brain of a person in anticipation of doing math

Brain of a person who is told that they do not have to do math ever again in their life

If not calculus or math, then what? What do we want our students to gain from their education?

knowledge• specific, for their job • general, as a life-time benefit

skills • clear thinking• logical reasoning • abstract thinking • interpretation of information presented visually• presentation of information using a variety of media• spatial reasoning• communication clear and precise of ideasetc.

Many of these can be done in chemistry, geography, biology, philosophy, language, social science courses!

Make these courses truly interdisciplinary and include some math

Keep in mind the users of math vs math experts populations

What math is needed for this ? How to interpret this diagram?

Logical thinking, connecting information

What kind of weather does this location have in summer?

Geometry can be taught via architecture

Social sciences, humanities – patterns, geometric thinking, visualization

Peak break-up times based on facebook (UK data)

Link to animated graphs

Why not use ready-made software?

This is also math …

Teaching math and making it relevant in 21st c requires action well beyond the boundaries of mathematics (math within interdisciplinary landscape), and beyond the boundaries of academia

Adjust courses in disciplines other than math to align better with perceived skills and knowledge required in 21st c

Change attitudes toward, and improve and promote vocational education – stream students out of high school into vocational training and education

Reform high school curriculum in grades 11 and 12 accordingly

Math 1C03• basics of mathematical thinking, simple investigations, simple proofs, etc. in the fun context of number theory and baby cryptography• how to approach a theorem?• narratives – exercises in writing precise math statements

Math 1MP3• investigating mathematics using computer programming in Python• investigate gaps between prime numbers; write a code for various numeric techniques (bisection, Newton’s method Euler’s method) and apply to suitable problems; investigate probability using simulation, etc.

What can we do within math departments?

Math 3G03Advanced problem-solving and investigations

• finally working on some geometry!• investigate open-ended questions, such as Collatz (3n+1) conjecture• investigate random walk• fun integration and finite and infinite sums problems

Math 3ET3Experiential education – high school placement

• practical component (preparing lesson plans, observing a teacher, helping students on individual basis, teaching, preparing tests, etc.) under guidance from a placement supervisor

• theoretical component (reading and analyzing math education papers on themes related to the placement)

• diary/log of activities (reflective piece, to judge where the student is with regard to the learning objectives defined at the start of the course)

Math 1LS3/1LT3 Mathematics for Life Sciences

… in a moment

as well, in my presentation at 12:30

Learning portfolio [under construction]

To provide an opportunity for reflection to students in math and stats, and as evidence of their academic development (potential benefit: reference letters)

Combination of math and narratives [blueprint]:• Starts will 10 “impossible” math problems that students work on as they progress through courses• Notes from math seminars, colloquia, etc.• Notes about courses (what are three things I learned in this course?)• Notes about interesting math, or math-related themes• Etc.

Math Departments should:

Offer rich experiences – early - to students that go well beyond calculus and linear algebra

Emphasize the importance of probability and statistics (offer more courses?), due to their increasing presence in our lives, in research and in applications

“Real-life applications”

How did it all start?

Math textbooks started introducing …

Example of a career application:

“We have to learn science because … North America will need N science literate people …. We need citizens who know science …”

So far no success - in spite of magazines, television, internet, etc., not many people are well informed about science and its impact on their lives

Often “scientifically informed” citizens do not make right decisions (living in suburbs, buying big cars, big houses, etc.)

Things are more complex

To start: remove almost all “real-life applications,” “career applications” and the likes from math curricula, as they make little sense and have nothing to do with real jobs. Keep good, interesting story problems.

High school courses are so boxed that they prevent interdisciplinary approach (why isn’t math part of other courses?)

There are plenty of meaningful applications

• Life sciences• Big data• Environment, climate change• Nanotechnology• Bioengineering, bioinformatics• DNA sequencing• Computational cell biology• Etc. but it is impossible to approach these topics (and many other) with little and/or inadequate math

Math 1LS3/1LT3 * MATH FOR LIFE SCIENCESwhat is the right math for life sciences students?

I looked at many math/bio papers and tried to identify what kind of knowledge and thinking would help students read and understand math in those papers

These insights suggest changes in math content taught. For instance:

• DEs are important, especially qualitative analysis of DEs

• Approximation of derivatives and discrete versions (Euler’s Method) and use of computers (ideally)

• Some several variables and PDEs (at an intuitive level)

• Reduce limits; no formal definition; use numeric approach instead of L’Hopital’s Rule

• Discuss relevant limits such as x^n/e^x to compare rates of increase (long-term behaviour)

• No series, no power series – instead, use Taylor polynomials (approximations are important)

• No Mean Value Theorem nor some other theoretical topics

• Include as much probability and statistics as possible

Teaching strategy:• start will simple models/ applications right away• build more and more sophisticated models as soon as math permits• use life sciences questions as motivators for teaching more math

Meaningful applications:• BMI• Growth of bones• Cancer cell growth (benefits of mammography)• Radioactive decay and dating techniques• Analysis of blood stains• Absorption of drugs (caffeine, alcohol, recreational drugs• Model of competition between two species

• Feeding patterns of animals• Shape of a honeycomb• Logistic dynamical system • Volume of heart chamber• Surface area of Lake Ontario• Computed tomography• Diffusion

and so on

Which functions to graph?

Creative tensions between real life and math

If you don’t eat vegetables you will not get ice cream.

Two television commercials for Head & Shoulders shampoo have been criticised for implying that the products leave hair 100% dandruff-free.

Procter & Gamble … [100% dandruff-free claim means] not visible to another person from a distance of two feet.

Sticking by its two feet measurement, Procter & Gamble said this was a "realistic personal distance" for people speaking to each other.

[source: BBC News Online, Tuesday, 4 April 2006, 23:07 GMT 00:07 UK]

Why “service” teaching is essential …

Many scientists/ researchers do not do math right

Study Finds 3 out of 4 Climate Science Papers Use Flawed Statistical Analysis http://www.libertariannews.org/2013/08/04/study-finds-3-out-of-4-climate-science-papers-use-flawed-statistical-analysis/

Statistical flaws revealed in top journals' papers (flaws in Nature and British Medical Journal)http://www.newscientist.com/article/dn5051-statistical-flaws-revealed-in-top-journals-papers.html#.Ui_Snbx69Q8]

Study: A Lot of Mind and Brain Research Depends on Flawed Statisticshttp://bigthink.com/Mind-Matters/study-a-lot-of-mind-and-brain-research-depends-on-flawed-statistics

Applications:

we need to do it seriously, or not do it at all (“if you don’t know what to do just take the derivative”)

keeping in mind that in many ways this is what students will retain (for their own good) and might actually use

Thank you!lovric@mcmaster.ca