Showing posts with label Pedagogy. Show all posts
Showing posts with label Pedagogy. Show all posts

Sunday, June 15, 2014

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.

Wednesday, June 11, 2014

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?

Monday, June 2, 2014

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.

Sunday, June 1, 2014

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.

Thursday, May 29, 2014

Students Appreciate Organization & Planning

I have found that one of the things that students appreciate (and recognize) most is a well-planned and organized course. Here are some student survey responses to the question, "What are the best things about the course?":
  • The course is phenomenally structured. It is clear and well organized with time to work in class that is hugely helpful. The learning is great!
  • The organization and the fact that I know what is due the next day and the following month via Moodle.
  • Everything is very organized and clear. There is a lot of things I can do to review and I never forget past lessons. I also have never had math so clear!
  • I believe the best things are the organization of the topics and the structure of the class. The pre-made notes and the explanations are very convenient and helpful as well as the time that is usually left after the lecture is over.
  • The course is difficult but extremely well planned and we've kept pace, giving me more confidence in how prepared we'll be. 
  • Everything is always perfectly organized (I love the way Moodle is set up and the daily class notes) so that we can plan ahead and get feedback before, for example, turning in the first drafts of the IA.
Students expect teachers to have their act together - and they know it when you don't (trust me, I have heard them talk about some teachers who are clearly planning by the seat of their pants - not kind). They appreciate it when you do your job well and are the first to point out (to other teachers) when a teacher is dropping the ball.

Teachers really should take the time to get their courses superbly organized (at least one week in advance). Their students know the difference between well planned and not.



Wednesday, May 28, 2014

One Reason I Love Teaching Mathematics

One of the most satisfying parts of being a math teacher is to watch students begin the year unmotivated and "hating math" (an unfortunate reality during my time as a high school math teacher) and see them end the year motivated and proud of the work they have done, with a positive outlook and renewed excitement about their ability to succeed in future math classes.

Some teachers aspire to teach the upper level classes with the "best" students (make no mistake, I enjoy teaching these classes too). But, the most personal gratification for me comes from my work in my lowest level course - Integrated Algebra & Geometry (IAG). It is there that I think that I really have the greatest impact.

Today, I sent e-mails to the parents of two of my IAG students letting them know that their daughters had the two highest scores on the most recent test. Both of these students entered the year at the very bottom. Other teachers had commented that they were "challenging". I passed one of these students this morning in the hall and told her that she had gotten a 94% on the test. Another teacher walking in next to her actually said out load in a somewhat shocked voice, "Really?"

Over the year these two students (and others like them) have slowly started to have a little fun in math class and have begun to earn small victories. They managed to successfully complete their assignments, and they managed to submit work on-time and get full credit. They quickly learned that there was someone there to help them when they got stuck and to answer their e-mail at night as soon as they had a question. Every little bit of positive reinforcement they received stuck and further enhanced their self-confidence and desire to succeed in mathematics.

As the momentum of these small successes took hold it became even easier to keep it moving forward. The students kept working harder and harder, and wanted to experience more success (for themselves and, I like to think, a bit for me). They knew I cared about them and in return they wanted to show that they appreciated it and did not want to "let me down". This may sound a little self-centered, and it is only an hypothesis, but it rings true with my experience.

Yes, there were times I wanted to strangle each of them and there were also times that I was disappointed with their occasional lapses back into past, unproductive behaviors. But, at those times, I subtly (and usually with an edge of humor) let them know that I was disappointed. However, my actions always showed that I continued to care and that I still had confidence in their ability to succeed in my class and in mathematics.

Every year this same process (which I would like to make more formal) repeats itself with many of my previously low performing students - of course, more with some than with others. I think the process is enabled by the following actions:

  • Genuine care and interest in seeing students succeed in mathematics
  • Unwavering confidence in their ability to succeed in mathematics
  • High expectations of the quality of work from both students and myself
  • Excitement about mathematics in general, and a willingness to share it with students
  • Sense of humor and willingness to make math class fun, flexible and engaging - but serious too
  • Many opportunities to practice, improve and succeed - repeated as needed
  • Constant, timely (near real-time) feedback on performance and meeting (or not) expectations
  • A chance to recover when mistakes are made - and they are!
  • Availability to help - in class, throughout the school day, and online outside of school hours
  • Constant reinforcement - both with the students and their families
  • ...and others that I have not yet nailed down.
This is a fascinating topic that I intend to come back to in future posts.

Monday, May 26, 2014

Lost Article: Is It True That Some People Just Can't Do Math?

I spent about 30 minute tonight looking for an article from the past (I had forgotten the name) titled, "Is It True That Some People Just Can't Do Math?" by Daniel T. Willingham. Interestingly I found the article I was looking for embedded in a very recent article by Grant Wiggins titled, "Conceptual Understanding in Mathematics".

I first read the original article when it was published in 2010 but had lost track of it. During recent discussions at school there have been multiple lapses into the "concepts vs. facts vs. procedures" debate. I always felt that this article aligned with my personal thinking and experience on this topic and wanted to find it and share it with everyone. It is worth the read!

Is It True That Some People Just Can't Do Math?

Sunday, May 25, 2014

Using Facebook for (Math) Courses

I started using Facebook as a communications tool for my courses about 2 months ago - as an experiment. I had previously been using Moodle and e-mail (both of which I still use) as my primary means of online communications with students. Although both worked they were cumbersome to use and did not really motivate students to read the content or take part in online conversations about math and education. Hence the experiment with FB.

I setup a FB group for my IB math (SL & HL) classes and sent an invite to all class members. I had not used FB groups before. I found the setup and administration easy and students could join the group without having to become a FB "friend" (which I do not do with students).

I immediately realized that this experiment was going to be a hugh success since:
  • Every class member already had a FB account and all joined the group within the day/week
  • All class members could post and respond to messages with comments
  • There was immediate feedback on who had viewed each post ("Seen by...")
  • Class members (and I) could seamlessly post math-related content from any web page ("Share on FB") and any device (computer, mobile...)
My courses now use FB for many tasks, including:
  • Posting course announcements
  • Posting assignment and assessment information
  • Posting reminders, hints, and other "immediate" content
  • Students post questions on assignments - and help each other online. This is great because it (1) gets them to write about math, and (2) let's everyone in class read, or better yet, actively take part
  • Students and I post math-related content, including articles, math jokes, links to useful sites...
It is a wonderful way to engage students in math outside the classroom and the possibilities for ways to use FB for the classroom are endless.

Some screenshots of a few examples are below.

Problem Posts & Discussion



Test Summary


Link to Article