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.

Tuesday, May 27, 2014

More from Daniel Willingham

After getting a reminder (and some motivation) from the practical writing and insight of Daniel Willingham in "Is It True That Some People Just Can't Do Math" I went out searching for more. There are other great articles and videos by Willingham on his personal site Daniel Willingham.

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?

Practice & Timely Feedback - Online Assignments in Moodle

Students appreciate timely feedback on their work and know that they need to practice to get better at math. Feedback not only allows them to know whether they understand something but it also motivates them to continue to improve. One of the ways I provide practice & timely feedback in my math classes is by using Moodle online quizzes.

The daily online activity focuses on content from the current topic but always includes review problems from past content. Review problems are randomly selected from over 400 existing problems (2-3 problems a day turns into a lot over time). I do this in both my Algebra and IB Math SL courses. An example question in Math SL is shown below:

Teacher View of a Moodle Question - Student cannot see correct answer.

As you can see, this student spent approximately 12 minutes working on this problem - with repeated attempts prior to determining the correct answer. Students can retake assignments multiple times until they get a perfect score. Not surprisingly, they spend a significant amount of time outside of class working on mathematics - and they truly enjoy it. They also appreciate the fact that they are getting constant reinforcement of concepts. There will be almost no additional review of material needed prior to our upcoming end-of-year assessment because they have been reviewing the material all year long! Feedback from students in a recent survey:
I also like the fact that in most tests there tend to be some review problems, which, again, forces us to go back and review previous material and have it always "fresh" in our minds (I wish this was done in more classes).
I really like how the quizzes are set up because even though it does take some time to complete them, they really do help and it serves as a sort of review and challenge. I also like how you can go back to the questions you missed and work on them. 
The takes time to develop the Moodle questions! If you don't enjoy technology then it's probably best not to start down this path. If you do enjoy technology and are interested I am always looking for collaborators to help extend my existing question banks and to try them out at other schools.

Common Core Suggestions for Intervention

I stumbled across the section "Supporting Students" while reading the Common Core (CC) - Appendix A on designing math courses to align with the CC. I was particularly intrigued by the Response to Intervention practices. Few of these suggestions are in place at my school...although we are looking for ways to put more support outside of the classroom in place gradually over the coming years.

---- from Appendix A of Common Core for Mathematics ----

Supporting Students

One of the hallmarks of the Common Core State Standards for Mathematics is the specification of content that all students must study in order to be college and career ready. This "college and career ready line" is a minimum for all students. However, this does not mean that all students should progress uniformly to that goal. Some students progress more slowly than others. These students will require additional support, and the following strategies, consistent with Response to Intervention practices, may be helpful:
  • Creating a school-wide community of support for students;
  • Providing students a "math support" class during the school day;
  • After-school tutoring;
  • Extended class time (or blocking of classes) in mathematics; and
  • Additional instruction during the summer
Watered-down courses which leave students uninspired to learn, unable to catch up to their peers and unready for success in post-secondary courses or for entry into many skilled professions upon graduation from high school are neither necessary nor desirable. The results of not providing students the necessary supports they need to succeed in high school are well-documented. Too often, after graduation, such students attempt to continue their education at 2- or 4-year post-secondary institutions only to find they must take remedial courses, spending time and money mastering high school level skills that they should have already acquired. This, in turn, has been documented to indicate a greater chance of these students not meeting their post-secondary goals, whether a certificate program, two- or four- year degree. As a result, in the workplace, many career pathways and advancement may be denied to them. To ensure students graduate fully prepared, those who enter high school under-prepared for high school mathematics courses must receive the support they need to get back on course and graduate ready for life after high school.

Furthermore, research shows that allowing low-achieving students to take low-level courses is not a recipe for academic success (Kifer, 1993). The research strongly suggests that the goal for districts should not be to stretch the high school mathematics standards over all four years. Rather, the goal should be to provide support so that all students can reach the college and career ready line by the end of the eleventh grade, ending their high school career with one of several high-quality mathematical courses that allows students the opportunity to deepen their understanding of the college- and career-ready standards.

Sunday, May 25, 2014

Why Innovative Educators Should Look Down Upon "Look Up"

I saw the original "Look Up" video about a month ago.

There were messages that I could relate to but there were also some points that I felt the video missed about the value of social media. Lisa Nielsen hints at the flip side of the video in her post.

Why innovative educators should look down upon "Lookup"

A challenging issue that will definitely get more press as time passes. But in reality, the technology is here to stay, and we must figure out the best ways of using it and its future incarnations.

Facebook Focus: Rate of Change

Today, a student in my Algebra class was confused about what rate of change was and how to calculate the rate of change given the measurements for two quantities. The problem she had was:

Rather than respond directly to her e-mail I posted the following general response to our FB group. My response was:

This comment was also posted to my IB Math SL class that is about to begin an introduction of calculus. A very useful 10 minutes spent discussing a very important concept with two of my classes via FB. We'll see what type of student comments are generated, either in class tomorrow or later tonight online.

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

Getting Started - Motivation

OK, to be honest, I have attempted to maintain a blog of my thoughts and experiences related to teaching math numerous times. I get started, write a few posts, then lose interest. This time I am going to take a slightly different tact. My goal is to post something, anything, at least once per day. Every day something interesting or thought provoking seems to occur. Maybe I try something new in the classroom or online that works or doesn't, or maybe a colleague does something special or frustrating. Whatever it is, it is typically worth my time to write about and reflect on. So here I go...

A quick introduction...

I am a high school math teacher at the American School of Madrid in Madrid, Spain. I have been teaching mathematics for 7 years and worked in the consulting industry for 20 years prior. I love teaching math and using technology to augment my teaching. I focus on IB mathematics courses, but have also taught Algebra, Geometry and remediation courses. I have taught in Montana, Japan and now Spain. I live in Montana during the summers.