High Expectations and The Art of Teaching

In working with educators over the past 15 years, a common theme tends to arise when we approach learning and rigor. I have been asked (and I once asked as a teacher) countless times, what about kids who “can’t” do the work? What if they are “3-grade levels behind” or “score on a kindergarten or 1st Grade level” on standardized tests? I’ve had many tell me that “our kids can’t do that.”

TNTP published The Opportunity Myth , a research study which identified four key areas needed for students to flourish. These included:

  1. Consistent opportunities to work on grade-appropriate assignments
  2. Strong instruction that lets students do most of the thinking in the lesson
  3. A sense of deep engagement in what they’re learning
  4. Teachers who hold high expectations for students and truly believe they can meet grade-level standards

I’ve changed my reply to these “what if they can’t…” questions over the years and now ask, “but what if they can?”

The importance of high expectations cannot be underscored enough. Countless research studies have focused on just that. In the Opportunity Myth, TNTP calls it out as one of the four determining factors of student success, but many others such as NCTM, NCSM, Hattie, and Marzano all cite similar research findings.

First, we have to reassess the deficit-based model that has been so prevalent in the education system since the enactment of No Child Left Behind. When we look only at student deficits, we fail to see their brilliance. Once we make the shift to noticing what students can do, it becomes less about filling gaps and more about supporting them through the art of teaching.

I would challenge educators to question the purpose and usage of standardized tests in our systems. Standardized tests were never meant as instructional tools. They were designed to determine which students were meeting grade level standards, and which were not. They do not give a true picture of the whole child and when making instructional decisions, it is incredibly important that we look at multiple data sources; data sources that are frequent and actionable.

The Art of Teaching

As our district continues the journey of implementing Illustrative Mathematics (a problem based curriculum), I have noticed that the art of teaching has never been more important.

When students are given tasks with multiple entry points and multiple solutions, teachers can shift their attention to supporting students in the moment instead of “after the fact.” We can empower students to access grade level mathematics instead of only reacting to instruction by the creation of multiple intervention groups. Are there times when small group intervention is the necessary? Absolutely. However, there are many more effective ways for teachers to scaffold and support students with learning gaps while engaging in grade-level work. Here are a few ways teachers can use their art and expertise to support students in grade level work:

  • Crafting questions to use the following day to reveal new strategies
  • Selecting students to share their work that might support the next step for other students
  • Providing a math tool or graphic organizer to support students as they work
  • Forming a small group to revisit a task and discuss strategies or introduce a strategy
  • Allowing students to revisit and revise their work

Crafting Questions

When I know what students know, what strategies they are comfortable with, and what connections they are or are not making, I can carefully craft questions to advance their thinking. For example, a student is drawing a picture every time they are asked to add (combine) groups. I could ask, I wonder what that would look like if you used numbers instead of pictures? Why don’t you try that and I’ll come back to see what you come up with.

For more on crafting questions, see Taking Action: Implementing Effective Teaching Practices in K-5 Mathematics.

Selecting Students

Another great way to progress student thinking is to select students to share a strategy that another student might not have thought of. For instance, in the scenario above, I might ask a student (B) to share that used a diagram or expression to find the sum and ask how his representation and that of the student (A) who drew a picture were the same and different. Or I might ask student A to check in with the student B and talk about their strategies. These interactions can take place whole class using the 5 Practices, or in partnerships or gallery walks.

Math Tools and Organizers

With the adoption of Illustrative Mathematics, we set students up to engage in tasks that allowed The Standards for Mathematical Practice to be part of each learning experience. There are many ways that utilizing the practices allow students to engage in grade-level work, but let’s zoom into MP5: Using appropriate tools strategically.

There has been much discussion in the math world for many many years about the inclusion or exclusion of math tools when students engage in mathematics learning. The emphasis on knowing math facts from memory has caused instruction to halt in order to “make students ready” to engage in grade level content. In fact, the memorization of basic facts continues to be a stumbling block in many classrooms, including special education classrooms. In fact, this quote from Strengths-based Teaching and Learning in Mathematics lays it out clearly: “If some experts have described algebra as a gatekeeper for the high school student, fluency with basic facts is the gatekeeper for the elementary school student who struggles – particularly a student with disabilities.

There is a myth that without basic facts retrieval, students cannot engage in higher level problem solving. I wonder what would happen if we allowed students access to tools that take that limiter out of the mix? For instance, a student who is working with fraction equivalency needs a calculator to multiply the numerator and denominator by the same factor (2/2, 3/3, 4/4) to look for patterns and generate equivalent fractions. I’ve witnessed on many occasions that students gain fluency with facts, BY engaging in grade-level activities such as this.

The world is changing, you would be hard pressed to find a job available today that does not use software programs, assistive devices, resources, or tools to support the mathematics we do on the job. In fact, our state has already included the Desmos calculator on all sections of our test for grades 6-8 and end of course exams. So has ACT, SAT, and AP exams.

Graphic organizers are another great support for students. For more ways to use graphic organizers to support productive struggle, check out Productive Math Struggle: A 6-Point Action Plan for Fostering Perseverance.

Small Groups

There will be times when we notice that several students are stuck and need an extra nudge or an opportunity to explore concepts further and may want to pull them together for a small group discussion. For instance, I notice four students are confusing addition and subtraction. I’m not sure if it is vocabulary, conceptual, or operational so I pull them back and we work with groups of counters. I cover two sets and tell them how many are in each set and ask how many there are altogether. I use this as a formative assessment to determine my next steps with them in the group.


Revision is so important in teaching for mastery. For too many years, math classrooms have given the big end of unit test, teachers grade it, and it goes home. Students need to have opportunities to see their mistakes, revisit them, and revise them. If the goal is mastery, we must live our words. I have seen this play out in many ways in classrooms.

  1. During a number talk, a student hears another students strategy and says “I’d like to revise my answer.”
  2. Or during a group discussion when a student group shares their work and another student notices a mistake in their own and asks if he/she can go back to their desk and revise their problem.
  3. A teacher hands out a unit test and meets with students individually to go over their work. She tells the students that she is available to conference with them if they would like to revise their tests and resubmit.

Great teachers use these opportunities to show students that they are teaching for mastery by allowing for review and revision.

The art and expertise of teachers has never been more critical. Students come to use with varied lived experiences, strengths and goals. It is our privilege and opportunity to help them flourish in our math classrooms through access to high quality, grade level tasks and high expectations.