Paul Kates – Centre for Teaching Excellence Blog

Fiction, Fun and Fractions – Paul Kates

Today I’m recommending some holiday gift books for youngsters in late primary school through to high school — books that weave together, as the title of this post suggests, fiction, fun and fractions. Each book finds its own way to free math from the classroom and bring it into the richer world of life and imagination to let children see and explore some of the magic, surprise and beauty in mathematics. It is my hope that some of the anxiety children may have about math will be replaced with fun and wonder.

Number Devil: a Mathematical Adventure by Hans Magnus Enzensberger, 264 pages.

Robert, a boy of 12, is visited in his dreams by a cheeky devil who likes to talk about mathematics, which is not one of Robert’s favorite subjects at all. But Robert begins to like his imaginary discussions with his nightly visitor and comes to understand more of the mathematics he has seen before in class. Over 12 nights of dreaming the devil shows Robert a wide range of mathematics topics (e.g. fractions, Fibonacci numbers, primes, series, etc) each explained in simple and engaging ways. And that is the goal of the book: putting fun and math together.

The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan, 256 pages.

This is a book that can be read aloud to a young child or read alone by anyone who enjoys an Arabian Nights fable. Thirty-four bite-sized episodes in the life of Beremiz Samir, The Man Who Counted, charm you with their elegance in both story and mathematical expression. Each episode presents an opportunity for the wise and learned Beremiz to call upon his mathematical ability to help someone in need or outwit troublemakers. The very young will enjoy the adventures alone until they are old enough to take interest in the simple, engaging puzzles embedded in the heart of each story, for this is a book to be read more than once.

The Math Olympian by Richard Hoshino, 482 pages.

This book is aimed at students from middle school to high school. Students who like math will learn a lot about problem solving to help them in their studies and maybe inspire them to enter the world of mathematics outside the confines of school. The book is constructed around five contest-level math questions. In trying to solve the questions, the main character, Bethany, passes on her mentors’ advice about how to understand mathematics. But the book is more than a very good primer about problem solving and math contests.

Students who don’t like math will be drawn into the story if they have a friend like Bethany, someone who does enjoy math. Bethany is excited about problem solving. She puts her heart into doing the thing she loves and dreams about, becoming a Math Olympian. At the same time, Bethany is growing through her teen years like all her friends. The book is Bethany’s story, told in her own voice, about a struggle that many teens will find overlaps their own stories in different ways.

Letters to a Young Mathematician by Ian Stewart, 224 pages.

In a series of 21 fictitious letters to Meg, Professor Stewart addresses questions about the nature of mathematics and mathematicians, and how to succeed in an academic career in university mathematics, from undergrad to tenure. With humour, common sense and insight the book answers many questions of interest and concern to students:

Why do math?
How do I learn math?
How do I create math?
How do I teach math?

My reason for including this book is to help students who are moving from high school to university and need to know how they can do well in their new, more challenging environment. The first half of the book is meant for them.

I hope you find something in this book list to interest a youngster who likes to be read stories or an older child who may or may not be too keen on math. I hope the readers find the charm, delight and passion in these books that I see.

P.S. Allow me to add a book list site named Mathematical Fiction you may not have heard of that caters to works of fiction about mathematics and mathematicians.

Learning to Learn – Paul Kates

New undergraduates are already successful students when they arrive at university. They come with learning habits developed over a decade’s time at school where “work harder” is a commonly followed injunction for improvement or to remedy declining achievement.

But learning at a university is more challenging than high school. Students face increasing rigour combined with more and denser material all at a quicker pace. Can students at university work smarter, making better use of their limited time? Continue reading Learning to Learn – Paul Kates

UW STEM Education and Mobius – Paul Kates

Back in August 2016 my colleague Tonya Elliott from the Center for Extended Learning wrote a post on Online Math Numbers at Waterloo, and Comparative Judgments as a Teaching Strategy in this space.

In that piece Tonya talked about the thousands of UW students who have taken online UW math courses and of the recognition of excellence received for the educational resources in these courses. Today I present more information about the new online environment named Mobius first introduced there. This platform offers authors and students expanded opportunities for rich, interactive learning.

As examples are three UW-Mobius project collaborations (CEMC, CEL) with the evolving Mobius system available free to the public:

uw open math mobius site — http://open.math.uwaterloo.ca

cemc university of waterloo — http://courseware.cemc.uwaterloo.ca

uw open eng mobius — http://open.engineering.uwaterloo.ca

To get a feel for what Mobius can do I’ll describe and link to specific features from each of these sites.

In the Chemistry for Engineers course you will see short (approx 5 minutes) narrated videos and animation. Live self-check concept questions using the ordering question type let students know which part of their answers are right or wrong. Other locations in the course make use of the Maple mathematical engine underlying Mobius allowing students to check their skill at doing calculations. These questions provide a motivating hint if students feel unsure.

The Linear Algebra1 1 Open Math site is designed differently, offering longer 20 minute presentations alternating with live quizzes. Each quiz question has its own template for generating tens or hundreds of different question variations giving students the chance to repeat and master the material.

The example chosen from the CEMC site is an interactive demonstration of the cross product of two vectors. On screen controls allow students to manipulate the size and orientation of two vectors while displaying the vectors and their cross product. This is an example of a Mobius math app. Math apps are great for letting students visualize concepts, experiment with dynamic objects and explore what-if questions.

UW has created thousands of questions for use in our Math, Physics, Chemistry, and Engineering courses. They are all freely available to use in any course you teach. As are the many Math apps on the Maplesoft Math app gallery page and on the Maplesoft shared content Maplecloud web site.

If you are curious about Mobius and want to learn more there is a hands-on seminar in two weeks (Thu Mar 2 11:15 AM), part of CTE’s very popular EdTech week.

You don’t have to wait two weeks though. If you have an idea for a Math app and want help realizing it, want to browse through the question banks, want to see how a lesson is created or just want to play around with Mobius then please get in touch.

Paul Kates
Mathematics Faculty CTE Liaison
pkates@uwaterloo.ca, x37047, MC 6473

Crowdmark – Online grading for large courses

This Fall 2016, the University of Waterloo will have 25 courses with a class size of between 500 and 1000 students and 10 courses of between 1000 and 2000 students.

The amount of paper handling to administer the potential 33,000 final exam papers from these large courses will be monumental. (For fun, guestimate the volume of paper this amounts to.)

The Mathematics Faculty has been successfully experimenting for a year with a online grading system called Crowdmark, a company founded by Professor James Colliander of the Mathematics Department of the University of Toronto.

Professor Colliander was faced with a similar problem: grading 5000 Canadian Open Mathematics Competition (COMC) papers each year with 100 volunteers. As with final exams, each paper is typically graded by a number of markers so keeping track of which questions are graded on which papers and when the papers are free to be passed to another marker is a time consuming and error prone business.

Crowdmark (CM) attempts to eliminate some of the time and trouble spent managing the grading process. We are not talking about a quiz system with automatic grading. Crowdmark is hand-marking done online. Skilled people still grade, and tests and assignments are still created for printing on paper so there is nothing new in this part of an instructor’s routine.

So, what is it that makes the marking process more efficient when done online?

Markers are able to grade the same paper at the same time. No more locating and waiting for a paper that someone else is grading. Or waiting for a batch of papers to arrive at your location to begin your stage of grading. Grading can be done concurrently at multiple locations and times.
Grades can be automatically summed, collected, summarized, distributed and recorded in a Learning Management System without needing to check for arithmetic or transcription errors.
No time needs to be spent returning piles of exam papers.

There is a time and money cost to using online grading. The physical papers have to be scanned into digital format (PDF file) before grading can start. High speed scanners (500 pages per minute) can process 1000 10-page exams in 20-30 minutes once delivered to the scanning machine.

Here I’ll briefly discuss how instructors and students use CM.

Steps for an instructor:

upload one test or exam pdf file into CM (leave 2 inches blank on the top of each page for CM ID info and set 1 question per page)
- CM duplicates the test pdf for each student and adds a paper and page ID to each page
download from CM the pdf file of student tests and print it
after the test scan all written test papers into a pdf file and upload the file into CM
- CM arranges the pdf file pages into a grid pattern: each row holds a student’s test pages
each marker clicks on a page in the grid to read, comment, and grade it
- when grading is complete page grades are summed for each test paper by CM
match each test paper cover page student ID with a student name in your CM course (assigned seating at UW can eliminate this step)
you choose whether CM sends each student their grade and a CM link to their graded test paper or to keep the grades and graded papers private and just download the grades for inclusion into a course grade

Steps for a student:

write the test paper by hand as usual
may receive an email from CM with a link to a CM page showing their test results

The links at the end of this post provide further details about Crowdmark. In addition, 2 live sessions demonstrating Crowdmark are coming up at the end of August and the beginning of September. The first is an introduction to Crowdmark on Wednesday August 31 and the second follows up a week later on Wednesday September 7 (1:30-3 PM) with details about a University of Waterloo system named Odyssey that works with Crowdmark. Odyssey organizes test papers, students and exam room seating providing relief from some time-consuming management overhead.

Crowdmark is not a free service, but the University of Waterloo has a licence so there is no charge to individuals (instructors or students) at the university.

If you are interested in learning more about online grading for your course please get in touch with me.

Paul Kates
Mathematics Faculty CTE Liaison
pkates@uwaterloo.ca, x37047, MC 6473

Intro to Online Marking using Crowdmark: Wednesday, August 31, 2016 – 10:30 AM to 11:30 AM EDT
Crowdmark home page, help pages and youtube channel.
UW Odyssey Examination Management

Early Student Feedback — Paul Kates

Feedback from students doesn’t have to wait until the time of end-of-term course evaluations. Getting feedback early and often in a course allows you to build on what’s working and make changes towards what can work better, all in time to have an impact on your students.

Asking students at the start of the term about their expectations for the course, the lectures, the textbook even their own work habits can give you an insight into why your students are in your course and let you address expectations immediately should they be out-of-line with the way the course is going to be run.

Eric Mazur in his book Peer Instruction gives a start-of-term “Introductory Questionnaire” to his Physics class where he asks

What do you hope to learn from this course?
What do you hope to do with this new knowledge?
What do you expect the lectures to do for you?
What do you expect the book to do for you?
How many hours do you think it will take to learn all you need to know from this course? Include everything: lectures, homework, etc.

(This and the following set of questions are attributed to Prof James Sethian, Department of Mathematics, University of California at Berkeley.)

With the answers in hand he addresses each of the questions in class – supporting and encouraging his students and expanding on student answers with his own goals for the class:

I want the material we cover to be useful to you beyond the exam. I want you to become good critical and analytical thinkers, able to tackle not just familiar problems but also unknown new problems or questions. Not only to plug numbers into equations but able to develop new models and theories, to make qualified assumptions, and then use those models and assumptions to break new ground in science and technology.

He also has the opportunity to address student expectations, realigning and influencing those expectations about the lectures, text and workload.

He gives a sample reply to all the questions above (ask me for a copy), but here I’ll only quote the answer to the question
What do you expect the lectures to do for you?

There were many very thoughtful responses to this question, but I did encounter a number of misunderstandings about the lectures that I should address to avoid falling short of your expectations. The most serious misconception I encountered is that the lectures will present and explain the fundamental concepts, while the book will clarify the ideas presented in the lecture. This is not what is going to happen. You will be reading the material before coming to class. The book will introduce the basic terminology and definitions, hopefully raise some questions, perhaps even confuse you a little (“to wonder is to begin to understand”). The lectures are intended to challenge your thinking and thereby help you assess your understanding of the concepts you read about, to further and deepen your understanding of these concepts, to stimulate and inspire you, and to show you how things “fit together.” The book will then provide further reference. In addition it will be a source for questions and problems.

Some of you expect to practice problem-solving in lecture, but problem-solving is not the main focus of this class. I want you to understand things, not just be able to “plug and chug.” This is clearly reflected in the way you will be tested – take a good look at the exams in the back of the syllabus. Close to half of the questions on each exam are not the traditional, quantitative problems you may have seen before. The solutions to many of these don’t involve even a single equation. Rest assured, the sections and homework assignments will offer ample opportunity to sharpen your traditional problem-solving skills. The lectures are meant to stimulate your thinking, to further your basic understanding. I guarantee that a better understanding of the concepts will improve your problem-solving abilities, whereas the reverse is not necessarily true. Here is what I think of some other answers given: …

After a month Prof. Mazur uses the following questionnaire to gauge how students are settling in to the course. This is another early opportunity to address concerns, misunderstandings and expectations.

What do you love about this class?
What do you hate about this class?
If you were teaching this class, what would you do?
If you could change one thing about this class, what would it be?

If you have your own in-course questionnaire and want to share it I’d be happy to use it along with any comments you care to include in a follow-up post.

Piazza – part 2 – web-based discussion forums for university courses — Paul Kates

Introduction

Back in January 2012 I wrote about Piazza, the free online Q&A site used by instructors for teaching. Since then, Piazza has grown even more popular with STEM subjects. Piazza reports that over 1000 schools and 300,000 students have participated in online discussions using their system. Continue reading Piazza – part 2 – web-based discussion forums for university courses — Paul Kates

10th Annual Desire2Learn Users Conference July 2013 — Paul Kates

The 10th Annual Desire2Learn Users Conference took place in Boston this year and I was lucky enough to attend. There were over 200 presentations throughout the three day event. I was drawn towards talks about mathematics and MOOCs – massive open online courses. You can find my notes on the talks I attended online.

Many of the presentations were recorded and most presenters provided slides. If you find a talk in the conference schedule or list of talks in my notes that you want to know more about please send me email at pkates@uwaterloo.ca.