By Jen McAleer, posted June 5, 2017 —

All students deserve a seat at the mathematical table. We should convince students every day that they do have mathematical ideas of worth. Estimation and notice-and-wonder tasks provide opportunities for all students to enter into the conversation. These low-entry, high-ceiling tasks can create an equal playing field. Students cannot know the answer to tough estimation problems, and no process to a solution is valued more than another; notice/wonder activities often do not reference specific questions, so there is no “it” to solve.

When I traveled to NCSM and NCTM this year, Christina Newell presented an Ignite talk that spoke directly to my thoughts and experiences with estimating. One of her major points was that students are naturally imperfect but often precise in their understanding and description of the world. Her example came from her child who struggled to find the words for a grilled-cheese sandwich, which became “Hot bread with the cheese of America.” Imperfect, yet precise.

Estimation can be used as an entry point into the imperfect, yet precise world of mathematics. The students I teach tend to struggle a lot with procedures and math facts. Their learning profiles set them at a natural disadvantage in a typical math classroom in which students memorize procedures and do twenty problems of the same type, over and over. These students often view quick computations and perfect answers as what it takes to be good at mathematics. In fact, they convince themselves that they are not good at mathematics and as a result do not find joy or intrigue in it. They learn math for the test and then it’s gone, and topics are never connected.

Estimation helps make sense of the world and helps mathematize one’s surroundings. Over time, students refine their ability to estimate and start to apply more of the mathematics that they have learned. Look at these two examples of the same task.

Estimation should not be a warm-up exercise or reserved for the end of the class. It should be the beginning of a conversation about deeper mathematics. It can be an entry point for students who typically are not welcome to the table mathematically because these students struggle with procedures and see themselves as being non-contributors to the class.

I am constantly improving my own approach to estimating the world around me. I am curious and intrigued by the world, and I use mathematics to be more precise in my estimations. I am not aiming for perfection; it is awesome to just get close to an answer. When I give an estimation activity to my students, it is not a one off, it is a conversation and an entry point into deeper mathematics. My goal is to have students walk away from my class and wonder about the math that surrounds them. Estimation is a way to do that. Let’s start inviting all students in our class to the table.

Jen McAleer is the head of middle school mathematics (grades 6–­8) at the Carroll School in Lincoln, Massachusetts. The Carroll School serves students with language- based learning difficulties who also tend to struggle with mathematics. McAleer has been teaching middle school for ten years and has a passion for giving all students a voice in mathematics and providing them with opportunities to be and feel successful while working with higher-level content, despite their struggles with procedures and computation. Reach McAleer via Twitter at @jennifuhs4.