Guest Blogger | Jessica Allen, Teacher of Mathematics in Puebla, Mexico

My optimism says that in 40 years my students will thank me. I long to transport to this future to confirm whether the work I do now will make a difference, but in my inability to time travel, I choose to trust the experience of the teachers whom I admire and who have gone before me. From them, I have learned that student gratefulness is usually retroactive, if it comes at all. But also, student attitudes and perceived learning in the present have little to do with the long-term rewards. Some of the greatest long-term rewards in teaching come through methods that access higher level or deeper level thinking, yet these methods often cause frustration and conflict in the moment. Regardless, the backlash is worth overcoming in order to bring about a deeper learning in education and richer character in students.

In classes where deep thinking is encouraged often, students may gain a flawed perspective of their own learning at the time that does not correctly reflect the efforts of the teacher. Students often view their own success in terms of how much they remember or how well they perform on short-term exams. If a student achieves well in the short term, they tend to see their progress and learning and applaud the teacher. However, learning is much broader than the short term, and as teachers, we are always looking to serve our students in the long term.

An example where this contrast between short-term performance and long-term understanding may be found is in the teaching of the Pythagorean theorem, which is used to find missing sides of right triangles. A teacher focused on more surface-level thinking that benefits students in the short term might teach the formula a² + b² = c² to their students and give a worksheet of triangles to practice with. Students are then expected to memorize a formula and apply it to situations that often have no context. However, another possible approach is to split students into groups and have them investigate relationships that present a discovery of the formula.

“Learning is much broader than the short term, and as teachers, we are always looking to serve our students in the long term.”

To start, each group has a long wooden board with various tape marks along the floor. Students choose a tape mark and stand their board at that mark. They then lean the board over onto the wall and now have a right triangle created by the floor, the wall, and the board. By using several trials, teamwork, and monitoring from the instructor, they find the relationship between the length of the board, the distance from the wall, and the height up the wall that the board touches. This type of activity requires exploration rather than memorization. By the end, students see triangles as dynamic figures whose sides’ lengths can change, yet the relationship between the sides remains the same. This is quite different from the other group of students who are given a page of rigid triangles and asked to find the missing side. That first group may perform better on short-term exams with worksheets, but in the long term, the second group has superior working knowledge to apply to future situations.

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Students often judge their learning by short-term assessments, which may lead to a misguided interpretation of their actual understanding. David Epstein, an investigative reporter, mentions an impressive study in his book Range: Why Generalists Triumph in a Specialized World. The study was conducted by the U.S. Air Force Academy and showed that students in calculus classes who did well on exams in the short term often recognized their learning and rated their professors highly. In contrast, students who did not perform as well on a short-term exam graded their professors harshly. However, the researchers looked at how well the groups did in follow-up classes with calculus as a prerequisite. They found that those who studied under teachers that focused on short-term success did not do as well in the long term as those students with teachers who took a deeper approach. (Epstein, 2019) This study suggests that students who did not perform as well in the instant were actually the ones who were able to develop a deeper learning of calculus that connected to other areas and subjects. The original perspective students had of their own learning and their teacher was perhaps misguided, revealing the narrow focus students have on the present. Teachers have greater goals than the present and therefore should not be afraid of student perception, but should continue providing deeper learning experiences for students.

Pushing students into deeper thinking may bring out their frustration, but it also allows them to make deeper connections and provides opportunities for character growth. As a student, it was hard to get used to my professors who pushed me to think deeply in class. I was used to waiting for instructors to supply solutions to questions, rather than pushing myself to work through them. It was hard to break out of the cycle of studying for a few minutes before an exam and getting all the multiple choice answers correct.

When my professors expected more from me during class, it felt discouraging at times, and I may have judged the professors unfairly. As teachers, we have the opportunity to provide rich learning experiences that push students beyond their comfort zone. Of course, they may feel frustrated because it is uncomfortable. Liz Grauerholz mentions this in her article Teaching Holistically to Achieve Deep Learning as she states, “Some students may be resistant to deep learning. It is hard work, and students must be highly motivated to do it. The type of learning discussed here, learning that often challenges one’s basic values, feelings, and beliefs, can be highly threatening to one’s sense of self (Grauerholz, 45).” She mentions the difficulty for students, which can manifest itself in various attitudes in the classroom. However, she also brings up why this transition is so difficult because it challenges a student’s self. As teachers, this is what we hope to access. In classrooms, are we providing an opportunity for students to grow in laziness or diligence? We have the capacity to help them to grow in creativity, teamwork, resiliency, clarity, and many more areas when we expect them to work hard and engage in deeper-level thinking.

Your class can be used to bring out a more holistic child and you should feel encouraged to provide opportunities for deep thinking in the class. Not only will you be able to teach a subject more profoundly, you are helping students to make connections with the material that will serve them for a longer period of time. When you reach for the long-term and deep meaning, you are also shaping a student’s character. Each decision you take in the classroom is an opportunity for a student to flourish. If we as teachers come together and encourage hard work, critical thinking, curiosity, etc., in our classes, then eventually the community will begin to see school as just as formative as joining a sports team. Do not be discouraged by attitudes or disrespect toward you from students and often parents. We, as teachers, have higher goals than our students can see.

For more on deeper learning, see Making Memories That Translate into Deeper Learning.

Epstein, David. Range: How Generalists Triumph in a Specialized World, Pan McMillan, 2019.
Grauerholz, Liz. Teaching Holistically to Achieve Deep Learning. College Teaching.V.49, 2,44-50. (2019)

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