Setting High Expectations
by Matt McLeod
“Whether you think you can, or you think you can't—you're right.”
—Henry Ford
This quote is attributed to Henry Ford in 1947, but it stems from a long history of ideas about mindset, self-fulfilling prophecies, and expectations. As a teacher, I adapted the wording to my context: “Whether you think they can, or you think they can’t, you’re probably right.” I learned the truth of this rephrasing during my early years as a classroom teacher.
I believed that all students could learn math and that it was my job to present it in a way that made sense to them. Yet this often led to me either breaking down difficult concepts into smaller pieces, making the problems less difficult, or showing them the exact process they needed to engage to find a solution. In other words, I was doing the work for them, and they were often just replicating what I had done. They weren’t doing the math, I was. I have since learned that this approach is dubbed “the soft bigotry of low expectations,” a phrase used to describe well-intentioned people who expect less from (and therefore try to do more for) students based on race, socioeconomic status, or background. Actions speak louder than words and what I was doing was lowering the bar for my students while claiming that I had high expectations for their abilities and their potential for success.
There have been many studies correlating teacher expectations and student performance. (See “Resources,” below.) One of the common findings is that students know whether or not their teachers hold high expectations for them and, not surprisingly, students do better when expectations are rigorous. Rachel Lambert, a teacher educator and researcher in special education and mathematics at the University of California, Santa Barbara, espouses this idea deeply and I quickly became a fan upon attending a webinar she led called “Trust in Their Thinking.” (In fact, the Math for All team is currently reading and discussing her book Rethinking Disability and Mathematics.) In addition to presenting many points that closely align with the Math for All approach, her overarching research finding is consistent and critical: When we believe in our students’ abilities to solve complex problems, they will rise to the occasion.
Enacting High Expectations
"Good teaching is more a giving of right questions
than a giving of right answers."
—Josef Albers
In the many years since I got certified as a classroom teacher, I have tried to embody the advice that the artist and educator Josef Albers offers in the above quote, with lots of help along the way. I try to be less helpful. I often present a good open-ended or open-middle problem that makes students think, ask questions, make mistakes, and struggle. For most of the problems I ask them to do, I have at least one solution path in mind as they work, but I don’t typically share it unless it is different from ones they discovered or created. I have learned a tremendous amount from watching how students make sense of and ultimately solve these types of problems. Because they know that I know they can.
My instructional approach prioritizes experience before formality and manifests my high expectations for students. This idea is in line with discovery and explorative learning as students are presented with a problem to solve before they have been taught a particular way to solve it. As students work through the problem, I pay attention to the different techniques they come up with, and, in line with NCTM’s Five Practices, I ask students to present their methods to their peers. During their productive struggle, I offer small hints when needed, usually in the form of a thought-provoking or reflective question, to prevent any student from getting to the point of frustration. Like any other routine or structure, this takes a great deal of planning and requires time before it is an established routine. You know you’re on the right track when you start to hear students say, “You know he’s not going to give us the answer.”
In their post-Covid blog series The Acceleration Imperative, the Fordham Institute offers several pedagogical techniques to consider as we work to maintain high expectations for students:
Technique |
Technique Description |
How it Promotes High Expectations |
| No Opt Out | Students are held accountable to always make an effort. | Students practice answering challenging questions and know that their teachers are not giving up on them. |
| Right is Right | Partially correct answers from students are not “rounded up” to fully correct. | Students receive the message that they are capable of getting an answer completely right. |
| Stretch It | OK/good verbal and written answers from students are pushed to be more robust. | Students are pushed to expand on “B” answers to make them “A” answers. |
| Without Apology | The teacher does not ever apologize for the material being challenging. | The students never hear from the teacher that something is too hard for them. |
From Theory to Practice
"Kids live up, or down, to expectations."
—Mae Jemison
During my sixth year of teaching, I taught a 7th-grade student named Jeffrey. That particular year, I was working to be less helpful, using puzzles, games, open-ended questions, and other such activities to promote more discovery-based learning for my students. In the fall, I heard a lot of “You’re not teaching us anything!” and “Why won’t you show us how to do this?” My responses were along the lines of “Because I want you to figure out how to do it. I know you can.” As the year progressed, I heard more “I wonder if this will work” and “Maybe we should try this” from students.
I remember Jeffrey partly because he was significantly taller than the other students, but also because he was the class clown. As our relationship developed, his behavior became less disruptive and he confessed that he never really enjoyed math class because it just wasn’t fun, so he never did well in math class. He was one of the students who really enjoyed puzzles, games, and trying to figure things out by himself. As he found his confidence, he learned that math can be fun and he became a cheerleader for other students when they struggled. One of my fondest memories of Jeffery was when he brought puzzles and problems to challenge me. I used some of them in my class. This told me that something was clicking. He was growing in part because he knew I knew he could.
I don’t pretend that everyone in the class that year thrived as well as Jeffrey, but I can say that their conversations turned from being about what I taught them to what they discovered and learned.
I hope this has encouraged you to believe that if you keep expectations high, believing that every student can engage in rigorous mathematics, and you get out of their way, they will astound you.
References
De Boer, H., Timmermans, A., & Van Der Werf, M. (2018). The effects of teacher expectation interventions on teachers’ expectations and student achievement: Narrative review and meta-analysis. Educational Research and Evaluation, 24(3–5), 180–200.
Papageorge, N., Gershenson, S., & Kang, K. (2020). Teacher expectations matter. Review of Economics and Statistics, 102(2). 234–251.
Same, M., Guarino, N., Pardo, M., Benson, D., Fagan, K., & Lindsay, J. (2018). “Evidence-supported interventions associated with Black students’ education outcomes: Findings from a systematic review of research.” U.S. Department of Education, Institute of Education Sciences, Regional Educational Laboratory Midwest.
Timmermans, A., & Rubie-Davies, C. (2018). Do teachers differ in the level of expectations or in the extent to which they differentiate in expectations? Relations between teacher-level expectations, teacher background and beliefs, and subsequent student performance. Educational Research and Evaluation, 24(3–5), 241–263.
Trinidad, J. E. (2019). Collective expectations protecting and preventing academic achievement. Education and Urban Society, 51(9), 1147–1171.
The contents of this blog post were developed under a grant from the Department of Education. However, those contents do not necessarily represent the policy of the Department of Education, and you should not assume endorsement by the federal government.
This work is licensed under CC BY-NC-SA 4.0 
Math for All is a professional development program that brings general and special education teachers together to enhance their skills in
planning and adapting mathematics lessons to ensure that all students achieve high-quality learning outcomes in mathematics.
