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.