Breaking the Legacy of Mathematics Struggles

Here are some thoughts on what a student who has historically "struggled at mathematics" should be looking for in a course that will help them improve and have a chance to succeed in mathematics longer term:

• A balanced focus on the "three pillars of mathematics":
• Concepts, 
• Procedures, and
• Facts
• The opportunity to practice...every day!
• A chance to develop an appreciation for the applications of math...everywhere
• A teacher they can trust and who is driven to help them succeed
• Opportunities for periodic successes
• Opportunities to have some fun in class
• Resource(s) to go to for help when they need it (possibly online)
• Opportunities to recover from mistakes (or, more likely, bad decisions)
• Support outside of school - from family and friends

I am sure there is more but these are my thoughts for this evening.

Printing Hell - IT Policy Run Amok

There is has been a dark cloud hanging over my school for the last year or so. Generally, the school is a democratic, trusting place where students and staff are treated with respect and where problems are addressed collectively, with all parties having a chance to take part in collaboratively developing workable solutions.

However, our  IT department, along with the support of senior leadership (not exactly sure who), decided that they would unilaterally enforce a misguided printing policy on all students and staff with the presumed goal of saving money. This policy was rolled out in an e-mail with little initial fanfare or reaction.

Although dictatorial, authoritarian, despotic, tyrannical, autocratic, undemocratic and arbitrary, the policy at first seemed mostly harmless, albeit irritating:

• Limitations on the size of print jobs - less than 20 pages for staff (even less for students)
• No multiple copy printing (same file cannot be reprinted for extended time period)
• Trimester total page limits (70 pages) for students (fortunately, not for staff)
• Cumbersome interface for submitting and approving color printing (and page limits for all)

With the passage of time, the policy has grown increasingly annoying for both practical and philosophical reasons. After a year, it has become an infected, festering sore eating away at my (and others) soul (and, no, I am not being melodramatic). Here are just a few of the many reasons why:

• When printing a test I occasionally (despite my best efforts at online proofreading) make a mistake on a page...that I usually see while walking back from the printer. I would like to fix the mistake and reprint the single page. But, no go, there is a timer preventing me from printing a file with same name again (even if only a page) within specified period. So, I am forced to rename the file in order to print the problem page.
• The IT infrastructure is fragile at best, with significant downtime and clunky rollouts of new technology. For example, recent work on a web server resulted in multiple system outages during the primetime of student and staff use (7-11 pm). Why this rollout could not wait until the summer (when school was not in session) is a mystery - since IT is reluctant to share their super secret (and convoluted) strategic thinking with the lowly rank and file staff. I mention this because having an organization that has shown limited success in running their own business tell me how to run mine (vis-a-vis the printing policy) is just flat out annoying...and it pisses me off each and every day.
• Students are being impacted in their ability to complete the tasks they are being asked to do. For example, one teacher recently asked students to complete eight past exams in preparation for an upcoming end of trimester exam. The teacher did not print off 50 copies of each past exam (approx. 15 pages each) but some students wanted hardcopies to do their work. Well, it is the end of the semester and their printing quotas are exhausted. You get the picture. (NOTE: This is a perfect example of where a less printing intensive approach could have been taken.).

But, what really gets me, is that we are an international school focused on trust, collaboration and most recently "international mindedness". We have very creative, bright students and staff who would willingly work together to come up with more internally motivated approaches to saving money and resources associated with printing, if given the chance. Unilaterally implementing a misguided policy on printing which negatively impacts the entire organization is contrary to everything the school stands for and works against the principles that we try to install in our students each day.

One final anecdote related to this issue. A student recently won election to the Executive Council of the student government on the platform of "fixing the printer policy". I wish him the best and will do everything in my power to help him succeed in making his election promise a reality. This is an issue we should be working together to address not one that is going to be solved via bureaucratic mandates.

Disclaimer: The point of view put forth in this blog post does not reflect that of my school's IT department or the school's administrative leadership.

On the Love of Learning?

I love math and all things related. I find articles discussing applications of math in science, economics, medicine, you name it, interesting. I love reading about famous mathematicians and scientists and the breakthroughs they have made. I love math jokes. I pretty much love all things related to math, science and technology. I also love my wife, teaching, biking, food, photography, philosophy, reading, computers...and lots of other stuff. What I mean by "love" is that I always find exploring new ideas interesting, I always want to do and learn more, not just while I am at school "working", but all the time. Honestly, I don't really differentiate between "work" and "non-work", it is all one big continuum. It is impossible to just turn off one and turn on the other...they merge together for me.

However, I can count on one hand the number of students who I have run across in the last seven years of teaching who truly "love" learning. I get the impression that many just want to succeed in school, they want to get good grades, they want to get into a good college, they want to make their parents happy...but seldom do they want to be at school to truly learn. There are exceptions, but most want to get out of school as quickly as possible (on a given day, at the end of the year, when they finally graduate). They are always looking for the next best thing...other than school. There are not many who truly seem to "love learning".

I am always looking for ways to make headway in unraveling this dilemma. Is it possible for the mass of high school students to truly love learning or is it a point of view that develops with time...like a fine wine?

Lifelong Learning & Summer Break

I just finished a rambling dinner conversation with my wife on whether and how students (and adults) like to learn. Earlier today, I wrote an e-mail to the parents of a number of my students letting them know about an online course offered by Stanford this summer, "How to Learn Math". While I was drafting the e-mail I kept thinking: "Most high school student are not going to want to take a class involving math over the summer. Will any of them (students or parents) actually see this course through to completion?"

This thought took me down numerous meandering paths of thought:

• Lifelong learning is meant to be interesting, fun and rewarding. Why do some students find high school the antithesis of this?
• Why are students fixated on getting out of school and doing anything but lifelong learning in the summer?
• What do I mean by lifelong learning? Does this learning necessarily occur in a physical building or during an online course? If not, when does it occur?
• Do students really shutdown for the summer or do they eventually get the urge to start structured learning before school restarts in the fall? Are they ready for school in the fall - even if they may not say it to a friend or an adult out loud?
• What would students do to learn if left to their own devices - without the formal structure that school provides? What would motivate them to push forward?
• With the Internet, there are many educational options available. I have shared numerous, interesting (to me) online course options for the summer with students in my upper level classes. Will even one student actually be sufficiently motivated to invest the time to complete an online course? Pessimistically, I am guessing not.
• What do students actually do with the 2+ months of "free" time during the summer? Is it all about sleeping and various forms of mental and physical stimulation?
• Do students still read books over the summer months?

OK, I know, there are not many tangible action items here, but it does provide some food for thought. I am genuinely curious about this topic and would love to put some more structure around understanding the role of summer break (or lack thereof) and how it relates to lifelong learning.

Accreditation - What Value Does It Provide?

Every school goes through a periodic accreditation process - often multiple, duplicative processes. I have been part of accreditation processes at schools in Montana, Japan and now Spain. This year my current school is completing the International Baccalaureate (IB) Diploma Program accreditation process as well as initiating the Middle States Association of School accreditation process for grades PK-12.

I do believe it is important that schools are accredited by a third party, but my issue/concern is that most staff who get involved in the process quickly become more focused on "completing the paperwork" associated with the process than with critically assessing the actual day-to-day functioning of the school and developing a detailed action plan focused on making the school better. Most action plans that get developed are put in place to meet the paperwork requirements of accreditation. They are then quickly forgotten...until the next accreditation cycle begins 5-7 years later. It is no wonder staff members are reluctant to take the repetitive accreditation processes seriously or to invest their limited time in taking part in accreditation teams and committees.

I am part of the accreditation team and process this year at our school. My goal is to try to keep a positive attitude and focus on completing the self-assessment critically and developing an action plan for the mathematics focus area that can actually be implemented and tracked over the next 5-7 years. Although I will be long gone, and the action plan may be quickly forgotten, I hope to do my part to critically evaluate how our school is doing in helping our students become better in mathematics.

Wish me luck!

Your Relationship with Students: Caring & Empathy in Teaching Math

Helping students learn math can be complex, difficult and requires a long-term commitment. It also requires that a "relationship" of trust be built with your students. Today I had about 20 different students in my room before and after school (as early as 7:30 am and as late as 5:00 pm). Interestingly, none of them were actually my current students. Many were students from past classes I had taught or students that I didn't even know. They had one thing in common...they all had a test in IB Math Studies coming up sometime in the next week.

So, the obvious question was, "Why were they coming to me for help?" There are many possible reasons but here are a few of the most likely (from my perspective):

• They trust me and are comfortable coming to me for help
• Their friends (who know me) told them I would help them and encouraged them to visit me
• They know I have confidence in them and want to see them succeed
• They want to understand the math and pass their class
• I am patient and explain mathematics in a way and at a pace that matches their learning style
• I give them an opportunity to practice and confirm/deepen their understanding
• I make the time working on mathematics enjoyable and fun - with a sense of humor
• And their course teacher is not readily available to provide help

I am sure there are other reasons (for example, desperation) that these student come to me, but I think this list is a pretty good start.

MORAL  OF THE STORY: Make yourself overtly available to work with ANY students on math (don't miss the opportunity). Show the students respect and that you care. Empathize with their situation and adjust to meet their needs. Make the visit to work with you productive and enjoyable. If you can do these things, over the long term, you will build a reputation with students for being a teacher who they can trust and a teacher who truly has their best interests at heart. This is something that takes (a lot of) time, and once established, every effort should be made to keep the relationship and reputation firmly in place. Best of all, it makes teaching math that much more rewarding!

IB Math SL & HL: Problems vs. Practice

Most of my students come to me in grade 11 for their first year of IB mathematics (either SL or HL). One of the big challenges I face is transitioning students from "practice" to "problems". I define practice as repeating the same skills over and over until you get good - for example, learning how to complete the square. "Problems", on the other hand, are new questions that require a student to combine multiple mathematical concept in new ways to work towards an answer.

Many of my students have been raised on "practice" but have limited exposure to "problems". This is a serious "problem" for them when they begin the IB mathematics curriculum. My assessments are almost entirely made up of problems, not additional practice. Early on it is not uncommon for a student to approach me after a test and say something along the lines of, "It's not fair, I haven't seen that problem before." Needless to say, I have little sympathy and proceed to explain the difference between "practice" and a "problem".

Eventually, they understand that it is going to be a real "problem" for them if they do not learn how to solve actual mathematical "problems". They come around, but it takes time and "practice". In the end, they eventually get a sense of what real mathematics is all about.

The Importance of Practice: Concepts, Facts & Procedures

Here is another article, Practice Makes Perfect, from Daniel Willingham that I found interesting. I highlighted a few points in the link provided. Some notable quotes:

It is difficult to overstate the value of practice. For a new skill to become automatic or for new knowledge to become long-lasting, sustained practice, beyond the point of mastery, is necessary.

Practice until you are perfect and you will be perfect only briefly. What's necessary is sustained practice. By sustained practice I mean regular, ongoing review or use of the target material (e.g., regularly using new calculating skills to solve increasingly more complex math problems, reflecting on recently-learned historical material as one studies a subsequent history unit, taking regular quizzes or tests that draw on material learned earlier in the year). This kind of practice past the point of mastery is necessary to meet any of these three important goals of instruction: acquiring facts and knowledge, learning skills, or becoming an expert.

Our ability to think would be limited indeed if there were not ways to overcome the space constraint of working memory. One of the more important mechanisms is the development of automaticity. When cognitive processes (e.g., reading, writing grammatically, reading a map, identifying the dependent variable in a science experiment, using simple mathematical procedures) become automatic, they demand very little space in working memory, they occur rapidly, and they often occur without conscious effort.

In mathematics, it seems clear that there is a mandate to develop automaticity in certain base facts and procedures. Failure to develop automaticity in their early years of mathematics is one of the primary roadblocks for students I teach in grades 10-12 and much of the time spent in remediation is focused on developing skills that should have been made "automatic" in earlier years.

There is much more in the original article and these points tie back perfectly to the early Willingham article I shared titled, Is It True That Some People Just Can't Learn Math.

Stop Saying "Balance is Key" When Discussing Technology

I have added Lisa Nielsen's blog to my RSS reader list...recommended. Here is a recent post on "balance" as it relates to using technology (for education & life in general).

The next time you find yourself afraid that the "overuse" of technology is a harbinger of the end of civilization as we know it, calm down. It is. But, behind those screens you might very well be surprised to find people who pursue their passion in a way that makes them most productive.

Stop Saying "Balance" is Key When Discussing Technology

Sunday Morning Moodle

Everyone has their own routine on Sunday morning. For me, it is time to update my teaching plan for the next school week, and work on assignments and online activities in Moodle - and today write a post for my blog. As the school year draws to a close, this morning I reflected on the work that I have put into Moodle this year for my IB Math SL Year 1 course.

I now have a complete course for year 1 (pre-Calculus) fully built out in Moodle. This includes all assignments, online activities and questions, and links to all supporting materials. The biggest chunk of work was related to building the question bank in Moodle to support the course. I just checked and my current question count is over 400 in the Math SL question bank. If I roughly estimate the average question takes me 15 minutes, then, conservatively, I have put in an extra 100 hours of work outside of school developing Moodle content - just for Math SL. And, I teach two other courses that require Moodle updates!

The good news is that (1) the Moodle content dramatically improves the ability of my students to retain and review content from the course, and (2) the work is now done at a level of quality that I am happy with - I won't have much new/redo work for this course next year.

So, looking back, it took a lot of time to get to this point. It has actually been a 4 year investment (with many 100s of hours of practice and improvement) since I started working with Moodle for my courses in Japan. But, I enjoy working with the technology, and I am now (finally) quite competent at using it.