The standard American kitchen consists of three types of people. Those who cook with love and measure from the heart, those who follow the recipe to a tee, and those who order out through their chosen delivery service instead. While observing my students complete math tasks, I predict which students fall into these metaphorical categories.
The students who “measure from the heart”… These students possess a natural grasp of mathematical reasoning skills. Providing understanding of why a given procedural method works magnifies their innate ability to create their own mathematical procedures and methods. Conversely, these students may feel challenged when prompted to explain their steps and methods, especially if their mathematical skills are underdeveloped. Insufficiencies bridging connections between everyday language and academic mathematical vocabulary to explain and defend their unique choice of procedures may be present. Such students thrive with a math instructor willing to provide guidance to facilitate and strengthen their ability to explain their thinking and organize their procedural methods. An intentional math teacher skillfully explains if their procedure is flawed and not rooted in mathematical reasoning, without destroying confidence in their innate ability to reason on their own.
The students who follow the “recipe box” to the tee… This student divulges in procedural math. Their motto is: Just give me the steps, and send me on my way. Their strong suit includes following and memorizing any algorithm. The gradual release, instructional method of, “I do, we do, you do” is their best friend. Beware, they are least likely to be a fan of the ‘productive struggle’ so pad rigorous tasks with growth mindset language and lots of accuracy check-ins. This student may feel challenged executing critical thinking tasks that are open ended and lack structure, even though the intent may be providing room for flexible creativity. These students require a teacher to encourage them to slow down and THINK about their math; as they can become so procedural they may utilize a calculator for basic operations they already know the answer to, but because they operate on a procedural autopilot may forget to think. Incorporating probing questions such as, “Does that answer make sense?” supports the strengthening of their mathematical reasoning skills. Consciously integrating estimation tasks to reinforce and add value to mathematical reasoning and thinking.
Lastly, there’s the “order out” student.. These are your “by any means necessary students.” They may appear to be winging it but they know what the end goal is. They take problem solving at face value and utilize whatever method makes the most sense whether it be procedural or thinking it through. They want to get it done and want the most common sense way to do it. Be mindful, during cooperative learning groups, this student may find it the most resourceful to outsource their problem solving to a peer for completion. These students need their math lessons to be practical and connected to a useful meaning in everyday life to buy into the value of learning mathematical reasoning or procedural fluency.
In the kitchen, the end goal is a cooked meal. Likewise in math class, the daily end goal is to achieve the day’s learning skill and objective. Just like in the kitchen, using different steps may affect the final product but the quality of the chef determines whether a different approach positively or negatively influences the final outcome. Similar parallels manifest in math lessons between the quality of the lesson and the instructor. Learning your students through observation and trial and error of diverse tasks makes way for intentional lessons to validate strengths and grow areas of weakness. A healthy classroom supports all of these learners by incorporating diverse instructional methods, learning activities, and assessments for all learners to both glow and grow. Inclusive, of tasteful cooperative learning tasks for these students to learn from each other.
The role of a math teacher must encompass the direct instruction the “recipe box” student needs to build confidence, while balancing a healthy portion of open-middle, critical thinking performance tasks for students who “measure with the heart” to develop and model their own problem solving strategies. Meaningful performance tasks and project based learning opportunities, will prompt your “order out” students to value the significance of learning concepts to use their reasoning and procedural skills.
Regardless of your categorical standing, many of us commonly experience a situation in which we thought we knew the recipe but had to go back to the trash can to double check the box. This often happens in math class as well. While solving an exercise students feel more confident after checking it over with the instructor or a friend to review their strategy. Or maybe our number senses are tingling and one can sense that a step was done incorrectly or skipped. I encourage students learning a new concept or procedure to adhere to the procedure and show all their steps because they are learning a new recipe. The first time you cook a new recipe you follow along with the instructions but, the 20th time you know which steps can be blended, which steps matter in sequence and which ones can be reordered without error. Learning a new concept and procedure in math class embodies this phenomenon. Teachers need to provide students with opportunities to “check the box” with their peers because problem solving just like cooking is more fun, engaging, and memorable when it is social.
Not big into cooking at all? These same principles can be seen for those tasked with assembling any type of furniture or equipment. Some of us follow the instructions, others just look at the picture on the box but, this project based metaphor remains a valuable tool. Nonetheless, your “measure from the heart”, “recipe box” and “order out” students all bring healthy valuable skills to the table. All learners need their styles validated to build mathematical confidence and can only gain from learning from their counterparts. Math educators who can observe and welcome all styles into their classroom are setting the table for success.