MathEd Forum

January 19, 2018

THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

FIELDS MATHED FORUM MEETING AGENDA
Theme: Mathematics and Equity
FEBRUARY 28
, 2015 at 10 am-2 pm
Fields Institute, 222 College Street, Toronto

 

10:00 AM - 10:15 AM Reports: OAME, OMCA, OCMA, CMESG, CMS, and other.

10:15 AM - 10:45 AM Iain Brodie (Toronto District School Board): REALLY Big Ideas in Data Management - Quantitative and Qualitative Research Done by 8-Year-Olds.

Abstract: Most big ideas in mathematics education revolve around the doing of math. Nowhere is this more apparent than in the data management and probability strand(s) where the big ideas are:
1. That students need to collect, organize, and display data.
2. That students should be able to analyze data using mean, median and mode.
3. That students should treat probability as being independent from data until they are too old to change.
What if we developed really big ideas? Ones that centred around understanding the relationships between mathematics and everything else in the world:
1. Data can be used to predict and inform.
2. Data can be used to reveal underlying patterns in the world.
3. If you really want to know the answer to something, collect a LOT of data.
4. The analysis of data absolutely involves probabilistic thinking.
This is the story of a class of young students who pursued the idea that there are answers to real questions to be had by understanding and using mathematics to discover underlying trends and patterns in our world.

Bio: Iain is a teacher. When asked what he teaches, he always responds with who he teaches. "I don't teach math, I teach children. They need to learn math." Treating his classroom as a laboratory, he and his students try to probe and discover the limits of what children are able to learn. They have not yet found that upper limit. Having spent the majority of his career teaching in the primary grades, Iain is finally teaching intermediate students where he has a wonderful group of teenagers who share his passion for good writing, integrating the arts, and indulging their collective curiosity about the patterns found in mathematics and science.

10:45 AM - 11:15 AM Egan Chernoff (University of Saskatchewan): Grand Probabilistic Delusions.

Abstract: It is a popular notion that probability is counterintuitive. Sir David Spiegelhalter perhaps said it best: "I often get asked why people find probability so unintuitive and difficult. After years of research, I have concluded it's because probability really is unintuitive and difficult." As one might expect, this notion has been fully embraced by a small band of researchers in the field of mathematics education; however, said research (and results) are not well known. As such, the purpose of this session is to provide a historical overview of the last 60 years of research investigating our grand probabilistic delusions. We will, of course, address and (not without debate) answer some of the perplexing probability problems found in the research literature.

Bio: Egan's research, in general, is focused on creating, developing and utilizing a variety of theories, frameworks, methods and models to investigate the teaching and learning of probability and probabilistic thinking. In particular, his research, currently, utilizes logical fallacies (e.g., fallacy of composition, appeal to ignorance and others) and particular models from the field of cognitive psychology (e.g., attribute substitution) to account for prospective elementary, middle and high school math teachers' normatively incorrect, inconsistent and sometimes inexplicable responses to a variety of probabilistic tasks.

11:15 AM - 11:45 AM Georges Monette (York University): Bayesians vs? Frequentists

Abstract: The famous statistician John Tukey (1915 - 2000) said that he had despaired of seeing the controversy resolved in his lifetime. Will it be in ours? Maybe we will come to see it as a fundamental duality whose resolution is in its acceptance. This talk will explore the roots of the controversy and some attempts to resolve it. Can we "bake the Bayesian omelette without breaking the Bayesian egg"? The moral is that you can't understand either approach without also understanding the other. The implication for education is that teaching traditional hypothesis testing and p-values without presenting their connections with Bayesian inference can lead to serious errors in statistical thinking.

Bio: I completed my Ph.D. under the supervision of Donald A.S. Fraser at the University of Toronto, who is one of the world's leading pathbreakers exploring alternatives and resolutions to the controversy between Bayesian and Frequentist inference. Although I've spent most of my career applying statistics and exploring the visualization of statistical concepts, I enjoy periodically revisiting the state of affairs between Bayesians and Frequentists.

11:45 AM - 12:15 PM Ayse Basar Bener (Ryerson University): Connecting Big Data and Data Science to the Statistics Curriculum.

Abstract: Data science incorporates varying elements and builds on techniques and theories from many fields, including math, statistics, pattern recognition, uncertainty modeling, data warehousing, and high performance computing with a goal of extracting meaning from data. It is a paradigm shift around the data, and the scope of analytics is descriptive, predictive and prescriptive. It is an interdisciplinary field that requires skills in math, statistics, machine learning, and computer science, software engineering and domain expertise. Statistics curriculum should focus on building fundamental knowledge in statistics and probability and also expand into building computational skills to derive models from data.

Bio: Dr. Ayse Basar Bener is a professor and the director of Data Science Laboratory (DSL) in the Department of Mechanical and Industrial Engineering, and director of Big Data in the Office of Provost and Vice President Academic at Ryerson University. She is a faculty research fellow of IBM Toronto Labs Centre for Advance Studies, and affiliate research scientist in St. Michael's Hospital in Toronto. Her current research focus is big data applications to tackle the problem of decision-making under uncertainty by using machine learning methods and graph theory to analyze complex structures in big data to build recommender systems and predictive models in health care, software engineering, smart energy grid, and green software. She has published more than 130 articles in journals and conferences. She is a member of AAAI, INFORMS, AIS, and a senior member of IEEE.

12:15 PM - 1:00 PM LUNCH BREAK (Light refreshments provided)

1:00 PM - 2:00 PM Panel Discussion on big ideas in probability and statistics education. After-lunch panel of morning speakers, Iain Brodie, Egan Chernoff, Georges Monette, and Ayse Basar Bener, will be joined by Skype to Jordan Ellenberg (University of Wisconsin-Madison) to further discuss connections of statistics and probability to curriculum.

Bio of Dr. Ellenberg (http://www.jordanellenberg.com/about/): Jordan Stuart Ellenberg is a Professor of Mathematics at the University of Wisconsin-Madison. He writes the "Do the Math" column in the online journal Slate and has authored a non-fiction book "How Not to Be Wrong" which is full of examples from the world of probability and statistics.

2:00 PM ADJOURNMENT


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