Students work cooperatively on a matching quadratics activity I designed.
I believe that all people can do math. What does it mean to do math? It means that you can notice and appreciate math in our everyday surroundings. It means that you have a good command of several conceptual ideas (ratio, area, input/output etc.). It means that you can perform several computational tasks (addition, division, etc.) with different kinds of numbers (decimals, fractions, signed, irrational, etc.) with fluency and precision. It means that you know when to use which method or tool in an attempt to problem solve. It means you are cognizant of your thinking and can reason analytically when needed.
I believe that math is the perfect discipline to train one’s brain analytically. It is highly procedural and simultaneously creative. In addition, math is beautiful and without race, ethnicity, gender, age, or sexual orientation. I believe that people who claim to never use what they learned in high school math class don’t realize that their everyday analytic thinking can be attributed to math. I believe teachers and parents need to emphasize the importance of learning how to think, regardless of affinity for a particular subject area.
I believe that math must be taught by direct instruction 70% – 80% of the time. Math is a language with many rules and few exceptions. I believe that students must not be expected to “make things up” or “figure things out for themselves”. While discovery and ownership is important, the reality is that we do not have unlimited time to cover prescribed content at prescribed depths. In the ideal world, we would have limitless time to have our students master concepts and procedures, but in reality this is not possible.
I believe that our country (the United States) does not value education. This makes recruiting and retaining good teachers, particularly in critical needs areas like math where people with that content knowledge could make more money in other fields, next to impossible. Furthermore, I believe that Americans feel that their success or failure in math is tied to a teacher or a gene, not to their individual work ethic. I believe that shifting a cultural paradigm is impossible for an individual to achieve. However, I believe that changing my students’ perspectives can be achieved in less than a year.
I believe that all teachers, like all students, are different and one must not expect to be an excellent teacher by just mimicking another excellent teacher. However, I believe all excellent teachers must have a strong content knowledge and must convey passion and enthusiasm for both their subject area and for their students. I believe that students will work harder for someone if they believe that person cares about them, and if they believe that teacher has a strong command of the subject matter.
I believe that assessment is not a bad word. I informally assess my students daily and formally assess them weekly and this gives me feedback on my teaching and gives them feedback on their learning. I believe that students must get results from formal assessments within 48 hours for the assessment to be meaningful. I believe that student assessment from outside sources is good if the assessment is well established, fair, and field-tested. I believe the Algebra I State Test and the ACT and the AP Calculus national exam are good assessments. I believe the Common Core State Standards assessments are valiant attempts at upping academic rigor nationwide, but I believe when the theory meets reality, modifications will have to be made. I believe that not all districts and students have equal access to technology, and if this is going to be a major force in the the next-generation CCSS assessments, equity issues abound.
I believe that student achievement is tied to socioeconomic status and thus I believe if one wants to compare growth and achievement nationwide, one must partial out the effect of money. However, I believe that though any statistician would agree with me, no politician is willing to admit it. Recently, studies have shown that not only is student achievement tied to socio-economic status, but growing up in poverty may permanently alter one’s brain. Given that we live in Mississippi, one of the poorest states in the nation, we as teachers and administrators may be working with more cards that we thought stacked against us and our students. The poorest paid teachers in the nation are quite likely beginning with the lowest students in the nation, and by the time these students reach high school, the die is already cast.
I believe that if a teacher guides his or her interactions with faculty, students, administrators and parents by keeping students’ academic growth and success at the forefront, then the teacher will be effective and successful.
I believe some of the aforementioned based on 23+ years of experience, some on relevant research, and some on both.
Math, Teaching, and Teaching Math 
Awesome. I related with all of it after just one year of teaching Algebra 1. Glad I read it because I thought I was alone in thinking that my class requires more direct instruction than others. Our administration has high expectation about the amount of time I should spend harboring cooperative learning in groups or projects. Don’t get me wrong, it is a great way to teach and I often have students work together, but it is generally frustrating for them and me. Like you said, we don’t have time to allow our students to “discover” every concept. Thanks For sharing.
I am not into groups and find taking energy to assemble them intrusive to my teaching time. In addition, many of the kids would rather have someone GIVE them answers. I choose myself to be their someone—but they WORK for those answers and I teach because I can! I am fortunate to work with some great colleagues of which, you Virge, are one.
Great stuff, Virge. I’m really glad to have met you this weekend, and I look forward to reading more of your posts, sharing stories and strategies, and mutually encouraging each other in this worthy task of teaching mathematics…onward! See you not only in June, but also at the next ‘jedi council’ meeting, in Boston. : )
When in college I lamented my liberal arts education and having to get grades as a measure of academic prowess, my parents always assured me that I was “learning how to think.” I believe this statement mirrors closely what you said about the flexibility of math education as it relates to thought processes. Yesterday, while estimating the height of a branch for a tire swing with my wife, I disappeared and returned with a yardstick, measuring tape and an iPhone. Compass app!! 45 degrees… it wasn’t until after I lined up the yardstick with the branch at a 45 degree angle that I realized I’d need to ‘splain it for my non-mathy wife. Didn’t get it, still asked where else I could measure it’s height from with a 45 degree angle. I said the opposite side… still nothing. It takes or it doesn’t, but most don’t give it the proper chance to take root. Anyway… I came up with 20 feet, then we emailed the vendor a pic of my wife standing under the tree with the yardstick on her head. Vendor came up with 20 feet. QED, or close enough.
Section III
I struggled to pin down a philosophy of teaching into one concise idea until I came across the
following from H. L. Mencken, “The best teacher of children, in brief, is one who is essentially childlike.”
There is an innocence to learning that seems to be lost through the years. You can see it in both my
nine-year-old son and my-one-year old daughter: the pure joy on their faces when they learn
something new. I think as educators we forget that this is how the reaction to all learning should be.
When it happens to a high school student in a mathematics classroom, it is an amazing thing. Seeing
that reaction in a young adult is the high that drives me to do better each day.
As Mr. Mencken points out, a teacher that can tap into their own childlike self can reach out for
that reaction. I have a passion for learning and many interests including mathematics. I feel it is
important to let that passion show in class often so the students remember that seeing connections for
the first time is a joyous thing. As a philosophy of teaching this does not dictate a style that must be
followed. As learners learn in different manners, I believe talented teachers teach in different manners.
By staying passionate and aware of the wondrous interconnectivity of our field, any lesson can be
effective whether it be direct teach, Socratic discussion, a group activity, student centered or any other
method. The desire for and enjoyment of learning in the right hands can make any style of lesson
engaging.
While I may have my preferred delivery methods, my childlike self also needs to be pushed to
play around. By differing how I teach, I recreate that enticing nervousness of something new and
uncomfortable. I force myself to explain things in new ways and learn more myself by varying
techniques or using new activities. Our calculus books have not changed in close to twelve years. To
freshen the experience for me and my students this year I changed the order of several topics. I am
following the course path of several popular textbooks, but I am having to modify my preexisting
materials and create new ones to bridge and circumvent topics seamlessly within our current textbook.
This has been a challenge at times, but it has made connections more apparent that were not there in
the past and pushed others into the background. Without the willingness and desire to feel like a
student myself again, I would have just kept things on cruise control for the year. I would have been
effective but I think my forced discomfort has made for a more engaging class for my students.
Section III
After nearly twenty-four years I have no problem getting up each morning to come to ‘work’. I
may have trouble waking up, but once I have achieved that, I still enjoy the challenge of each day. In
my Algebra 2 courses we have recently worked through material completely new to them. I am
excited by the fact that students will walk out of a logarithm lesson being able to effectively use and
define something they did not know existed ninety minutes before. Even better, many of them had
asked during the previous unit if there was a function to do exactly what a logarithm does. Not only are
they enjoying the newness of the material, they understood the application and usefulness of the tool
before they knew it existed. As children, we experience this, “wow, where was this before,” feeling
often. If as teachers we can create that feeling once a fortnight we can consider ourselves remarkably
blessed.
A common part of childhood is learning sports, musical instruments and other lifelong skills. Many
of these skills become second nature so that as adults we can pick up an instrument after years and
play songs memorized long ago or if we are very talented, play new compositions on the spot. Likewise,
the muscle memory of sports can come back very quickly when finding oneself in a gym or on a field.
To create academic experts, teachers must also run practices with drills and abstract portions of the
world pulled out momentarily to build memory and intuitive recall for their students. These are not to
punish or occupy the student, but to help capture that newness of mastery a child experiences as the
drill moves towards the recital or game. By connecting back to their own early learning, the childlike
teacher can break complex activities down into elementary parts that can be practiced and brought
back together later. Through careful planning and use of these types of activities the student becomes
more intuitive as to which skills to apply and when.
I guess when it also comes down to silly trivia, historical tidbits, bad jokes and fun observations I
will slip into my classes and letters of recommendation, it is my inner child driving everything I do for our
students and school. My philosophy, which I have been forced to consider at a length I had not in
decades, is all tied to my ability to let my inner child loose for eight hours or so each day. I also am glad
I saw that H. L. Mencken quote on the wall above my board.