Meet Them Where They Are by Dr. Natasha T. K. Murray

Dr. Natasha T.K. Murray is an educator, administrator, teacher educator, adjunct professor, researcher, professional developer, and consultant, who has taught on every level from elementary through graduate school and has served within the field of education in myriad capacities including as a New York State Leader for the National Council of Supervisors of Mathematics (NCSM); Phi Delta Kappa (PDK) International’s Board of Directors; President-Elect of the New York State Association of Mathematics Supervisors (NYSAMS); Penn Literacy Network (PLN) faculty; Professional Learning Team Facilitator for the New York State Master Teacher Program; on the Advisory Board of the State University of New York at Old Westbury’s School of Education; Editorial Panel Chair of Mathematics Teaching in the Middle School, a teacher journal published by the National Council of Teachers of Mathematics (NCTM); and as a Fulbright Specialist. She has been a proud member of NCSM for many years. (All views expressed are her own.) She can be contacted via her website and found on Twitter @poly_math_.

Earlier today, I was trying to get driving directions to an unfamiliar destination and decided to use my favorite navigation app: Waze. For some reason, it couldn’t find my exact location and told me to “proceed to highlighted route.” “Well,” I thought, “if I could find the highlighted route, I wouldn’t really need the navigation app, would I?” This got me thinking about education.

In ongoing discussions with numerous educators, we often talk about the best ways to help students expand and enhance their mathematical understanding; the overwhelming consensus is that we should meet the students where they are. To use a very simplified analogy, if we’re trying to guide a student from point C to point F, if the student is at point A, for the student to develop substantial and sustainable understanding, we must meet them at point A instead of starting at point C. (This would certainly be better than my navigation app telling me to proceed to the highlighted route!)

Many publications of NCSM and the National Council of Teachers of Mathematics (NCTM) also appear to be aligned with the idea that for students to make sense of the mathematics they’re learning, they need to “[develop] understanding of a situation, context, or concept by connecting it with existing knowledge” (Martin et al. 2009, p. 4, emphasis added). If connections to their existing knowledge are not present, authentic and enduring understanding will not occur.

In my varied roles within K-12 and higher education settings, I’ve conversed with numerous teachers about connecting instruction to students’ existing knowledge and experiences; often, they connect the idea of existing knowledge to prior knowledge and adjust their practices accordingly. It’s very important, however, that when we think about existing knowledge, we distinguish it from prior knowledge – though they’re similar, they’re not synonymous. I’ve seen countless lessons, in all content areas, where teachers quickly teach the prior knowledge they deem necessary for that day’s lesson. Though I agree with their intentions, teaching something quickly prior to the day’s main lesson doesn’t transform that newfound information into existing knowledge – existing knowledge is knowledge that has been solidified and concretized, it’s deeply rooted and not superficial. If it’s taught very quickly to support a more advanced or nuanced concept, it’s not likely to support or sustain enduring mathematical understanding.

Let’s say, instead of thinking about this in terms of teaching, we think about it as training someone to lift a 50-pound weight. If everyone in the class is expected to lift 40 pounds prior to the beginning of the weight-lifting course, and some students can only lift 20 pounds, it would be impossible to start them at 40 pounds. And, if their trainer tried to quickly get them from 20 pounds to 40 pounds, it would not only be unhealthy and unsafe, it would be detrimental to their growth.

In the classroom, though many educators agree we have to build upon students’ existing knowledge, this is much easier said than done. In practice, oftentimes when there is a confluence of challenges and constraints, it can be difficult to maintain this ideal. Many teachers have expressed to me various reasons why there may be a disparity between espoused theory and (pedagogical) practice(s) – in many educational spaces, there’s significant pressure to “cover the curriculum” and a general expectation to “get the students to pass” end-of-year exams regardless of the circumstances. These challenges may also be magnified in math classes where students have an increasingly wide range of interests, resources, and readiness and, especially in a year following 16+ months of interrupted instruction, the differences in access, engagement, and other mitigating factors are likely to make the range even wider.

While this adds to the multitudinous challenges of the classroom, there is still hope.

If we continue to embed practices that prioritize student interest and existing knowledge, heighten strategies for differentiated instruction, and maximize the integration of tasks that have multiple entry points, we can minimize the chasm between theoretically meeting students where they are and ensuring this is reflected in our pedagogical praxis. Continuing to develop and enhance these practices can increase the alignment between espoused and enacted ideals and, thus, support our cultivation of learning environments primed for each and every student.

For a list of referenced sources, visit Dr. Natasha T.K. Murray’s blog page.