Preferences on the Summer 2012 and FW 2012-13 course offerings

In keeping with the tradition of offering Math 5020 and Math 5400 (the two required courses for this program) alternate years we will offer History of Mathematics for Teachers (MATH 5400) during the Summer 2012 or FW 2012-13. One possibility that has arisen is that it should be offered in Summer 2012 (roughly 12 weeks in May through July, possibly Tuesday/Thursday but finer details such as dates are quite tentative at this point).

I don't want to take this option if this should conflict with people who have already taken Math 5400 and will leave them unable to finish until the end of 2013. If this should apply to you, would you please contact me and let me know what courses you have taken and your plans for finishing the program and I will try to take these into account when we decide what will be offered in the 2012-13 academic year.

FW 2011-12 schedule

We had to switch the days that Fundamentals and Algebra would be offered because of a conflict that I had. Sorry for those of you who signed up for the courses with the days switched.

The actual schedule is now.
Math 5420 6.0 : Algebra for Teachers
Ada Chan
Mondays 6-9pm

Math 5020 6.0 : Fundamentals in Mathematics for Teachers
Mike Zabrocki
Thursdays 6-9pm

In addition, I will be out of town the first two weeks of September and so the Fundamentals course may face a delayed start that we will have to make up. A notice will be sent out to registered students as we get closer to the start day.

A talk by John Mighton

I saw this talk by John Mighton a few months back and ended up showing it to my class. So many things that he said about mathematics and mathematics education resonated with my experiences and I thought it was worth sharing.

The Ubiquitous Bell Curve - a presentation recorded at the Perimeter Institute in Waterloo.

Testing and learning

As long as I was posting the note on upcoming classes I thought I would report on some research that I found interesting recently. A report in the Journal of Science by researchers at Purdue University finds that testing helps people learn better than a number of other studying techniques.

New York Times
The Huffington Post
The Telegraph

In another report in the journal of Science, researchers at the University of Chicago found that writing about test anxiety before the test helps students to relieve stress and do better on the test.

University of Chicago press
Toronto Star
Globe and Mail

Summer and Fall courses

Summer courses for the M.A. for Teachers program offered by the mathematics department.

It was only recently that the course Math 5430 6.0 was split into two courses, one on probability and the other on statistics. We will be offering them both this summer with two different instructors.

Math 5440 3.0 : Probability for Teachers
Neal Madras
Monday and Thursday 6-9pm May 2-June 9

Math 5430 3.0 : Statistics for Teachers
Steven Chamberlin
Tuesday and Thursday 6-9pm July 5 - Aug 4

Fall classes:

Math 5020 6.0 : Fundamentals in Mathematics for Teachers
Mike Zabrocki
Mondays 6-9pm

Math 5420 6.0 : Algebra for Teachers
Ada Chan
Thursdays 6-9pm

Education is currently announcing:

Fall 2011:
MATH 5920/EDUC 5215 3.0 : Research in Math Ed. with instructor TBA.

Singapore and Superman

An article in the New York Times indicates that a number of school districts across the U.S. are adopting a new math curriculum hoping that the latest fad will improve math scores. I don't (completely) mean to dismiss this sort of change by calling it a `fad.' I'm willing to support anything that works. But I worry that school districts make policies by picking and choosing to implement the easy parts of a curriculum and don't make the hard decisions.

A publishing company (SingaporeMath.com) sells books to 1500 schools across the U.S. This article in the New York Times focuses on one distinguishing aspect of the curriculum, that the students start by spending a full week of math lessons just on the numbers 1 and 2. They also mention some other features of the program which uses visual means to represent concepts (e.g. bar graphs and visual aids such as blocks and cards) and problem solving to help students learn in different ways. One great feature of this curriculum is that it seems to be roughly acceptable to both sides of the math wars.

An alarming quote from the article though:
``Mr. Thomas said that about a dozen schools had started and dropped Singapore math, in some cases because teachers themselves lacked a strong math background and adequate training in the program.''

The big buzz in the news these last couple of weeks is a documentary film that appeared at the TIFF this year ``Waiting for Superman.'' I'm anxious to see it but I have heard it is fairly dark and depressing. The movie makes a case that many schools in the U.S. school system are broken and one answer to fixing them is charter schools. One main complaint about the movie that I've heard repeated in several settings is that it seems to imply that charter schools are the magic bullet to American education problems even though they mention that only a portion of charter schools are more successful than their public school counterparts.

Links with High School in Paris

Someone I worked with a few years ago went to Paris to become a high school teacher there. He just wrote me a message today that I thought I would pass along:

> Notre lycée souhaite developper des liens internationaux avec d'autres
> lycées dans le monde pour éventuellement faire des echanges. Mes eleves
> iraient une semaine a Toronto puis les canadiens viendrait apres une semaine
> à Paris.
>
> Est-ce que tu penses que des high school teachers que tu connais dans ton
> programme à York seraient interessée (de préférence un high school
> downtown)?
> Il faudrait trouver un sujet commun d'étude pour favoriser le travail en
> commun entre les deux classes.

My translation:

Our high school wants to develop international links with other high schools around the world so that we would eventually create an exchange program. My students would spend one week in Toronto and then Canadians would come after for one week in Paris.

Do you think that high school teachers that you know in the York program would be interested (with a preference of a high school downtown)?
We would need to find a common subject of study to facilitate the work between the two classes.

---

If you or someone you know might be interested, contact me and I can get you in touch with my friend who wrote this message.

-Mike

My pet peeve

As this is a blog, I sometimes post comments about things I see in the media as well as announcements about the program. I just wanted to share with you this column that I found in the Detroit Free Press written to an advice columnist 'Dear Leanna':

"Dear Leanna: My seventh-grade daughter, Samantha, hates math. I told her that like most women, I wasn't good in math either, so if she got a D, that was OK. Her father is furious. He says she needs to do well in math to have options. She wants to be a dress designer. They need math?"

When I first read the question I was squirming in horror. Look away! '...like most women...' ???? Where does that EVEN come from? (don't answer that unless you really want to, I know very well where it comes from). Oh, the humanity!

That aside, at least the columnist addressed math attitudes (but seemed to brush aside the blatent sexism) and assumed that a 7th grader who decides that she wants to go into dress design would still have the same belief next week.

But Leanna didn't see the larger context in which math appears in design. She mentions "measuring, estimating, purchasing, budgeting, paying expenses, making a profit." That is only the part that involves arithmetic. But good design requires innovation and developing new technology and techniques. If Samantha were to restrict her skills to only those which do not involve math then she really won't have a deep understanding of how new materials are created and can be manipulated, she will have to rely on others to do that for her. Writing off math limits what you can do with a computer and knowing what a computer can even accomplish (you mean a computer does more than browse the internet?). There are an uncountable number of less tangible effects of being math illiterate.

Fall term classes

Hi All,
Hope you had a good summer. Classes start again this week and I thought I would send out a reminder and welcome back message.

(1) Classes will be 6-9pm as in previous years. We had to fight the registrar so if you saw listings that classes would be 7-10pm please ignore those.

(2) The history and 'fundamentals' course are offered in alternate years and this FW term Stan Kochman will be teaching the history course. Walter Whiteley will be teaching the geometry course and it has not been offered in a while (and will probably not be offered again for another 3 years).

(3) The GPD has asked me to schedule an advising appointment with all current students early in the Fall term. It will be possible to do this over the phone or before the Monday/Thursday classes and the purpose is to make sure that we both know of any courses that you will need to take before graduation (summer 2011 courses will be decided in the Fall and it is helpful if I know of any gaps).

-Mike

Its OK to register (finally!!!)

Sorry about the day about the ability to sign up for classes. The course should now be listed and you can register. Below is the announcement that Primrose just sent out.

---

All the course offerings for Summer 2010 are now on the Graduate Studies Lecture Schedule.

Graduate Students,

Please be reminded that the registration deadline is May 3, 2010 (see below). After this deadline, the Faculty of Graduate Studies will be charging a late fee of $200.

All important deadlines for graduate students is available at the Faculty of Graduate Studies webpage: www.yorku.ca/grads
It is your responsibility to be aware of these deadlines

Sincerely,

Primrose Miranda
Graduate Program in Mathematics & Statistics

Updated Announcements on Upcoming Classes

Upcoming summer courses offering by the math department for the M.A. in Mathematics for Teachers program:

May 10-June 16 (Monday and Wednesday) 6-9pm
MATH 5210 3.0 credits: Problem Solving I
by Yun Gao.

June 21-July 28 (Monday and Wednesday) 6-9pm
MATH 5500 3.0 credits: Topics in Mathematics for Teachers
on the topic of Naive Set Theory by Bob Burns.

---

For the Fall-Winter 2010-2011 terms the Mathematics department will be offering:
MATH 5450 6.0: Geometry for Teachers with Walter Whiteley, Thursdays 6-9pm
MATH 5400 6.0 History of Mathematics with Stan Kochman, Mondays 6-9pm

---

2010-2011 Important Dates for Graduate Students have now been published on FGS website, http://www.yorku.ca/grads/index.htm

---

The following announcement was sent towards the end of February and I am re-posting it here. If you did not receive this message, write me with an updated email and I will get you on any missing mailing lists I can.

February 22, 2010

Dear Graduate Students,

Summer Term 2010 registration begins Monday, March 1st, 2010! Be sure to register and enroll in courses early!

As a graduate student, you are required to maintain continuous registration in your program of study; this means you must register in each term (Summer, Fall and Winter) until you complete all the requirements of the degree as either full-time or part-time.

To register, enroll in courses and view the York course website, please go to: http://www.yorku.ca/yorkweb/cs.htm. The registration deadline for Summer Term 2010 is May 3, 2010, if you register beyond this date, a late fee of $200 will be applied to your student account. Therefore it is important that you register for the term early and enroll in courses early (if applicable).

Please note that unless your Graduate Program Director and the Dean of the Faculty of Graduate Studies have approved a change of status, you must remain in the category of registration to which you were admitted. To request a change of status (i.e. leave of absence, change to part-time, extension of time) for the Summer 2010 term, students must make their request through their Graduate Program and complete an Academic Petition Form or a Program Approval Form at least six weeks in advance of the start of the term.

For more information on; Registration; Important Deadlines and Dates; Faculty Regulations; Forms and the FGS directory, please visit the Faculty of Graduate Studies website at: http://www.yorku.ca/grads/.

The Faculty of Graduate Studies wishes you all the best in your academic progress and success in your current program of study, if you have questions, please contact your Graduate Program or the Faculty of Graduate Studies.

Sincerely,

Sharon Pereira

Someone else's presentation on the Multiplication Principle

There is a blog Math Notations that covers various topics about math. This weeks topic is titled "Counting, Multiplication Principle, Pigeonhole Principle and Reasoning for Middle Schoolers and Beyond."

I know I have a different perspective on this subject that many of you have been forced to see in Fundamentals, but one of the reasons I like it is that this idea comes up in almost every one of my classes at some point.

No matter what I teach, at some point I find myself arguing that the number of something is the product of two values and the reason is the multiplication principle. In number theory, this simple idea allows us to derive very deep results from drawing a few pictures.

Women over 40 good at math

An article in the Toronto Star from March 10 sites research from Graham Orpwood, a York University emeritus professor, that women over 40 do significantly better than men in college math courses. The article suggests that the difference might be due to better time management skills but it seems that that particular conclusion is more of a guess.

Toronto Star article

The study also says that half as many women study math as men. There was little attempt in the article to explain why this might be the case.

What I don't like about the Toronto Star article is that they then get a bunch of (apparently random) people to comment on the results apparently picking the narrative that the reader might take away from this study.

What is important are the three summary points of the conclusion of the study:

• Many students identified as being at risk of failing math have a poor grasp of basic functions taught in elementary school, such as fractions, ratios, proportions and percentages, so students should be provided more practice in these.


• College and school staff should hold a round-table discussion on how to streamline which high school math courses are required for admission to college courses and not have such a disconnect from school to school.


• Schools should convince parents and students to focus on time management and self-discipline.

It is hard to make such sweeping statements about gender differences over time, but data should be collected to see what the possible causes of large scale failings and shifts of attitudes towards math. I can say that when I was going through high school the number of girls in the advanced math courses were cut in half each year from years 9-12 until there were almost none in the calculus course in my high school. However, in the years after I was in school this changed dramatically. What this could mean is that in the next few years more women over 40 will start studying math. In my first year courses I see a roughly 50-50 split between the sexes.

Some states will allow graduation after 10th grade

Eight states in the U.S. are planning to participate in a program that will allow students to graduate 2 years early assuming that they pass the appropriate exams. The tests would cover math, history and science. The program is being introduce by the National Center on Education and the Economy.

The purpose of the program is to allow students who are interested in a vocational or college degree to not have to take the full four years of high school. Even if students pass the tests they may opt to during their junior and senior years of high school to take college prep courses Massachusetts decided not to implement the program because they felt it was aimed at students interested in vocational training and they already have a vocational program developed in their schools.

New York Times coverage

New York Times blog about a second chance at math

The New York Times is publishing in the opinions section a blog by Mathematician Steven Strogatz. The purpose of this series that he is writing is to take a look at math from elementary school to grad school for an artist friend of his who knows very little about mathematics. He hopes to introduce to this friend the meaning of what we say when we call a proof elegant and to convey the importance of mathematics.

In his first two entries he is starting with some very elementary ideas, numbers and arithmetic, but he intends to build up to bigger things. Already he has given a proof (using rocks) that

1+3+5+...+(2n-1) = n^2 .


Here is a TED talk by him about how synchrony arises from very simple mathematical rules and in nature.

Fear of Math passed from Teachers to (female) students

I have to admit that I am not one to acknowledge fear of math since that is far away from my experience. But there are plenty of websites that discuss math phobia and how to get over it.

example 1, example 2, example 3.

Now in an article in the Proceedings of the National Academy of Science researchers tested the hypothesis that fear of math is learned from elementary school teachers that have weak math backgrounds and that themselves have a fear of math. What they found is that fear of math seems to be passed onto the female students and not the male students. How this happens is not known.

The experiments were conducted by first measuring math anxiety within both the teachers and the students at the beginning of a school year. By the end of the school year, the more anxious a teacher was about mathematics, the more likely that girls (and not boys!) were to agree with the stereotype that boys are good at math and girls aren't.

One thing I did not know that 90 % of elementary school teachers are women (this is a statistic of U.S. schools, but I believe that it is probably similar for Canada), although I have spent some time in elementary schools here in Toronto and I should have been aware of that.

There are obvious followup questions such as "does fear of math get passed from male teacher to male students?" (which doesn't get addressed because the teachers this study were all female), and "does this only happen at the elementary school level?"

Here is some news coverage of this study:

A very short summary of the results from Chicago Public radio
NPR
Science News
Science Daily

Here is a 2007 story on fear of mathematics:
CBC - Fear over math marks reaches academic proportions

A couple of announcements

Important dates

I got the following message to forward on to the program. If you didn't receive it and would like to be added to the mailing list please let me know:

Dear Graduate Program Directors & Graduate Program Assistants,

Please be advised that the 2010-2011 Important Dates for Graduate Students have now been published on FGS website, http://www.yorku.ca/grads/index.htm.

About upcoming courses for summer session:

We are still waiting on final approval for the summer courses. We will be offering in the Summer 1 session (roughly May - June) "Problem Solving I," a 3.0 credit course with Yun Gao. Yun has in past years been responsible for the Putnam practice sessions for our undergraduate students.

In the Summer 2 session (roughly June - July) Bob Burns will be teaching a topics course on set theory using the book "Naive Set Theory."

Note that both "Problem solving I" and the topics course have yet to be approved so we have been slow to announce them.

About upcoming courses for FW 2010-11:

The mathematics department will be offering Math 5400 6.0: History of Mathematics for Teachers with Stan Kochman on Monday evenings 6-9pm and Math 5450 6.0: Geometry for Teachers with Walter Whiteley on Thursday evenings 6-9pm.

Winter 2010 Term Graduate Registration - Jan 15 deadline!

The Winter 2010 Term has begun, the Winter 2010 Term Registration Deadline is January 15th, 2010.

As a reminder, graduate students are required to maintain continuous registration and register in each term (Summer, Fall, & Winter) until the completion of their degree as either a full-time or part-time student. Students are expected to remain in the category of registration to which they are admitted, unless a change of status is approved by the Graduate Program Director and the Dean of the Faculty of Graduate Studies. Graduate students (continuing and new) are required to register for the Winter 2010 term by January 15th, 2010, students who register after the deadline will be charged a $200 late fee.
For more information on Registration go to: http://www.yorku.ca/grads/registration/index.htm.

Students who have not yet completed all the degree requirements, who are making academic progress and continuing with degree requirements must be registered for the Winter 2010 Term. Failure to do so by January 30th may result in the student being withdrawn from their program of study for failure to maintain continuous registration.

For information on Important Dates for Graduate Students go to:http://www.yorku.ca/grads/calendar.htm.

Program Overview

I will be announcing in the near future here on the blog some changes to the M.A. in Mathematics for Teachers program that have passed through some approval steps. I am currently waiting for some final approval by the Faculty of Graduate studies. The changes are quite minor on the surface, but include new calendar text, admissions requirements, degree requirements and significant changes to the course offerings.

In the past months I have found myself writing what this program is about over and over. Many of the times that I have written this program overview, the description goes into some document which is very unlikely to be read by anyone (and especially unlikely to be read by the students of this program). For this reason I thought I should record at least one version of this in electronic form. I also welcome comments on the following text. If you feel that it does not accurately reflect the reality of this program feel free to leave your feedback.

---

The M.A. in Mathematics for Teachers has been offered by the department of Mathematics and Statistics as a stand alone degree since the mid 1970s. The purpose of this program has been to offer an opportunity for elementary, high school and college teachers to increase the breath of their mathematical knowledge to give a broader context to the mathematics that they teach in their own classrooms.

Students are enrolled in the program on a part time basis. It is designed to welcome students that may have completed their university studies a significant time in the past. Courses for this degree are clearly distinguished through their numbering with the first digit 5 while the courses in our regular M.A. degree are numbered with first digit 6. In order to achieve the goals of the program, the requirements are more course intensive than our regular M.A. program. The range of courses offered for this degree gives students an historic perspective as well as chances to practice techniques of problem solving, writing, and presenting mathematics since these aspects of the discipline are relevant for teachers of mathematics at any level.

York University also offers a graduate diploma in Mathematics Education that may be taken concurrently with the M.A. in Mathematics for Teachers degree or an M.A. program with the Education department or as a stand alone diploma. The diploma focuses on mathematics education as an area of study grounded in critical examination of teaching practice, learning theories, and curriculum related to the teaching and learning of mathematics. It is designed to provide opportunities for graduate level study of theories and research in Mathematics Education and may be taken in conjunction with the M.A. in Mathematics for Teachers to prepare a student for study in Education at the Ph.D. level. Several recent graduates of the diploma in Mathematics Education have gone on to do graduate work in Education at York University and OISE/U of T.

This degree is part time program and classes are scheduled in the evenings to accommodate students who have employment teaching during the day. Prerequisites for the courses generally do not require that students have a recent training in mathematics, but the expectation is that the coursework will build on knowledge familiar to students that have had past experience in mathematics and are now required to teach mathematics. This program does not prepare students for study at the Ph.D. level in mathematics nor does it lead to teacher certification in Ontario.

Easy to state, hard to solve problem

One of the authors of the blog "Computational Complexity," William Gasarch, posted a computational challenge on November 30 and he is offering $17*17 = $289 if someone comes up with a solution. I like this problem because it is easy to state and hard to solve.

The n x m grid is c-colorable if there is a way to c-color the vertices of the n x m grid so that there is no rectangle with all four corners the same color.

For some good pictures of the definition see the blog: this blog posting.

Conjecture: the 17x17 grid is 4-colorable. (worth $289 if you prove this conjecture, worth nothing if you disprove it)

Theorem: the nxn grids for 1<=n<=16 are 4 colorable

Theorem: the nxn grids for n>=19 are not 4 colorable

William Gasarch is offering the $289 because "I REALLY REALLY THINK THAT IT IS 4-COLORABLE. I could still be wrong."

Here is a possible way to get students started on this problem:
1. Show that the 4x5 grid is 2 colorable. Here are some examples of the 2x2, 3x3, 4x4 grids.



Notice that once you have a c-coloring of an nxm grid then any subgrid of this gives a coloring of a smaller grid. Show that the 5x5 grid is not 2 colorable (hmmm, there are only 2^24 ways of coloring a 5x5 grid with white in the upper left corner).

2. Some extensions: How many ways are there of coloring the 2x2 grid with 2 colors? with 3 colors? with 4 colors? up to rotation and other symmetry? up to switching colors? Extend this to the 3x3. Can you extend it to the 4x4?

3. Find the mistake in the 17x17 grid below:



Hint: This 17x17 coloring was taken from here so this will give away where the mistake is.

4. Write a function (pick your favorite computer language) that tests if a c-coloring of an nxm grid is valid.

Any other ideas?