"As a man thinketh in his heart so is he." James Allen

Here is the ultimate essential question posed in a New York Times article titled When Math Makes Sense (To Everyone): To what degree are our beliefs about children’s abilities determined by the results of our current education system?

The article was a follow-up to a previous piece on Jump Math's founder John Mighton, who expressed some interesting viewpoints on education and math instruction.

“Our belief in hierarchies is producing the hierarchies.” In other words, our belief that some people are naturally better than others in some areas produces an education system characterized by hierarchies designed to sort students. Formalized academic tracks would be the most extreme example of these formalized hierarchies. A math curriculum gamed to ensure that only "gifted" students could take Algebra in eighth grade, and thus, prevents many capable students from taking calculus in high school, would be a less obvious, but just as insidious, example.

Using Mighton as a case in point, the article postulates that we may not know what we are capable of achieving. "As a youth, he (Mighton) was fascinated by math, but he wasn’t a natural. He almost failed his first calculus course. But he trained himself to break down complicated tasks and practice them until things that initially confused him became second nature. He went on to do a Ph.D in mathematics."

"Research on experts – whether in chess, cello or computer programming – indicates that natural ability is less a predictor of success than effort and deliberate practice. A big part of what we call “giftedness” is “task commitment” – and that can be encouraged."

My Take

Our beliefs act as our auto-pilot that drives our behavior. What we believe about the capabilities of students to learn and teachers to teach directly impact the approaches we take. We can quickly discover what teachers and schools believe about students by examining four areas, which gives us insight into both a teacher's and a school's auto-pilot:

1. Grading - A teacher's philosophy of grading reflects the teacher's beliefs about human nature and how students are motivated. In fact, one of my favorite interview questions for prospective teachers was to ask about their philosophy of grading. Their response told us more about them as a person and as a future staff member than just about any other question we asked.

Teachers who believe that work and effort predict student success use grades as a means of providing both feedback and encouragement to their students. Grades are viewed as a byproduct of learning. Their students understand that their grades are a reflection of their work and effort and that they have the power to change them if they choose to work hard enough and to put in the time needed to master the concept. These teachers view student learning as feedback on their teaching and they use that feedback to guide their instruction, to focus review efforts, and to target remediation, because in their classroom, the only way a student can fail is if the student either quits of gives up. Failure is not an option. Their students typically say that their teacher will not allow them to fail. They never give up on any student. These teachers often used standards-based grading practices that emphasize mastery. They believe that learning time is relevant and the outcomes and mastery is an absolute.

Conversely, teachers who believe that grades are a reflection of student ability, use grades as rewards and punishment and as a weapon hoping that the fear of failure will motivate students to do better. Instead of using student learning as feedback on their teaching, they place the blame for poor performance on the students. Review and remediation are not a priority for ability-driven teachers. If a student is doing poorly in their class it is because they "didn't do their homework," or they "don't belong" in the class.

Schools tend to take on one of these two belief systems or mindsets. They either believe that all students, given time and effort, can achieve to high levels or they believe that students are either born with "it" or they are not, and no amount of work or effort will raise them to high levels of achievement.

The school that believes in work and effort seeks to reduce course failures and to increase the number of students taking higher-level courses through enhancing their skills. Schools who believe that ability predicts performance resist efforts to reduce course failure or to encourage more students to take higher-level courses because they fear that they will have to "water-down" the courses to help students succeed in those courses.

2. Interventions - Teachers who view ability as the best predictor of success see no need to provide interventions because failure is viewed as a natural consequence. They believe that it is their responsibility to sort students and to weed out the capable from the less capable.

Teachers who believe that work and effort predict academic success view interventions as a natural part of their teaching and helping to raise student achievement. These teachers simply refuse to give up on students.

Ability-driven schools often have no 3. Math, or 4. Reading interventions for struggling students. When offering interventions for struggling learners, ability-driven schools do so begrudgingly. Conversely, schools that believe that time, work, and effort are the best predictors of student achievement, have numerous interventions in both 3. Math, and 4. Reading for students and some even go as far as to require students to attend extra sessions.

Final Take

The beliefs, attitudes, and expectations of teachers combine to form a collective mindset or school culture, which drives the behavior of individual teachers and schools alike. Four specific areas provide insight into those beliefs and mindsets--grading, interventions, math, reading. How teachers and schools view and address these issues are strong indicators of the school's culture.