How many times have you been teaching a lesson or explaining your content when suddenly the question gets asked - “When Am I Ever Going To Use This?” For some teachers, this question may spark a level of discomfort and may even have them asking themselves: when would a student ever actually use this?
The Usual Answer
As math teachers, we love to make sure students see our content as relevant. After all, we know math is EVERYWHERE and we want to communicate that to our students. Hence, it makes sense that when this question arises, teachers search for a few specific examples:
If you want to become a seismologist (they study earthquakes), you need to have logarithms to use the Richter scale.
For the future seismologist in the room, we may satisfy them with this answer - but chances are not all of your students are looking to be the next seismologists of the world.
How Is This Relevant To Me?
What we really want to think about when planning an answer to this question is how what we are doing in class will be relevant for students. When we respond with a very specific career example tied to an application problem, we reduce the number of students we reach. While every student can see the application, not every student may see its use in their future.
We hope we reach all students by the end of the course with application problems and contexts that have piqued their interest - but there is an even more important way that every student can benefit from this lesson. To explore this, we must first consider the overall purpose of math class.
What is the Goal of Math Class?
As teachers, we want to prepare students for the next phase of their lives. We want them to leave with great mathematical knowledge, but there should also be another goal that is even more applicable to their everyday lives. While there are many skills that we should teach them in preparation, the “Four C’s” are commonly acknowledged as the most important:
Critical thinking Creativity Collaboration Communication
As math teachers, we can give students the opportunity to practice these skills daily in each one of our lessons.
Critical Thinking
In the real-world, we want students to think through complex situations and develop their own solutions. When an unknown illness arises, scientists and medical professionals need critical thinking skills to rely on information from similar illnesses and new experiments to formulate cures. When a software engineer encounters a bug in a large piece of code, they must step through each line to look for errors and additions to improve performance.
As math teachers, we don’t want students to look at every problem and immediately say “I know how to do this”. We want their brains to get used to working through unfamiliar ideas and trying to make sense of them. Essentially, we want the students to learn that problem solving is what we do when we don’t know what to do. With practice overtime, this skill becomes more natural and important in a wide variety of situations.
How Do We Do This In EFFL?
Critical thinking is at the heart of every EFFL lesson. We want to encourage flexible thinking by starting them off in a new context and solving a problem that they are unfamiliar with. By asking a few scaffolded questions, students will discover a new solution and process for themselves.
When the students look at the activity, they should be able to get to work quickly. The first few questions are often reviewing something they previously learned. However, groups will then find that the familiarity of the questions goes away and they are being asked to apply these familiar concepts in new ways. This is where we want the groups to persevere through the challenge and never quit.
Testing ideas to see if something works is never a bad thing. We like to have the students look at their initial work as a “rough draft”. Problem solving can be messy. Help them keep the mindset that with each failed attempt they have learned something valuable - what doesn’t work. By reflecting on why it did not work, they can ultimately make the adjustments they need to so they can figure out what will.
Creativity
Developing a solution can not only be cognitively demanding but it can also require a lot of creativity.
We want students to put together past knowledge in new ways to create a brand new process that can solve new types of problems. We want them to get creative about how they arrive at a solution (think about multiple representations - creatively solving with a graph, equation, table). Creativity is encouraged by letting students develop their own process and ideas. When different methods show the same solution, it not only helps the students feel confident in their answer but also lets them see that there are multiple approaches that can work.
How Do We Do This In EFFL?
We see creativity in each lesson through the solutions students propose in the activity. As we walk from group to group, it is not uncommon to hear disagreements on how students want to tackle problems. If both ideas make sense, encourage each student to try their own idea independently. When both methods get to the same solution, have the students explain their ideas and discuss if they prefer one method over the other.
If you are not hearing multiple approaches being proposed in a group, it doesn’t mean that we can’t still ignite their creativity. Journey from group to group and see if each group is tackling the problem the same way. Chances are - you will notice some differences. When a group finishes the activity early, challenge them by referencing an idea that another group had and make them determine if their idea would work. This will help fuel the discussion in the debrief. Alternatively, pick a few of the questions and ask a quick finishing group to find a solution using a different method than they did the first time!
During the debrief, highlight the multiple approaches you have seen from individuals and groups. Allow them to compare and contrast these different methods - and as a class try to come to a consensus about if one is preferred over another. Often, one approach may be quicker and more direct (which we want to formalize so all students have it), but we also want them to understand that different solutions can still work.
Collaboration
In most job settings, employees will be expected to work with other people. Getting along with others, learning how to listen, receiving feedback, and suggesting ideas are all crucial skills for any area of work. In our classroom, we can encourage the same ideas by allowing the students to work together on problems and to share ideas. Many students come to see the benefits of talking through a problem or even how powerful it can be having multiple brains focusing on the same problem as opposed to one.
How Do We See This In EFFL?
A great EFFL lesson needs to be supported by a great classroom structure. We organize our rooms with the students sitting in groups so that they can work with one another during the class period.
After a quick introduction to the context, we release students to work in their groups on the activity. We like to encourage the “read, discuss, write” protocol to help groups remain with each other during the activity. One group member should read the question aloud, followed by a discussion period of them sharing their ideas and potential solutions. This discussion portion is where the collaboration magic should happen. Students should not only learn how to share their ideas but also learn how to take and give feedback on those proposed methods.
We want students to discuss and develop a deep understanding of each other’s solutions. By developing this understanding, they can help each other catch any flaws in their reasoning and make forward progress. By asking questions for clarity, it helps ensure that everyone in the room is learning - not just the one giving the ideas. With each suggestion, we want the group to move closer to a response that is built on a group consensus. Finally, once we have this response that everyone in the group agrees on, everyone should write it down.
Communication
Bridging from collaboration - we also want the students to be communicating their ideas effectively. This starts by us helping to add clarity to their ideas. Verbally, we as teachers can have the students begin thinking about this by asking them questions such as “What do you mean by that?” or “Can you explain more?”. As the students have these conversations, we continue to move them forward in how to explain their thinking and reasoning in writing. We want their writing to be detailed enough that anyone can take their work, read it, and understand how they arrived at a solution.
How Do We See This In EFFL?
As the students work through the activity and discuss their ideas, they will spend a lot of time defending and explaining their ideas to one another. As the teacher, we can be very involved with this as we check in on each group as well. If we scan the activity and see a number with no supporting work, it is the perfect opportunity to ask the group how they arrived at that. We want to point out that what makes sense in their head also should become clear to anyone on the outside trying to make sense of their solution. Reiterate that a correct solution is not just about the final value, but also about a justified method. We often have students write their work on the board, so it is really important that this work is presented clearly, especially if the group is presenting a unique solution that other groups have not come up with in their own groups.
If the supporting work looks good, don’t be afraid to ask a group to expand or explain the idea. Listen for their vocabulary use and being able to explain a concept multiple ways. These are all things we will want to touch on during the debrief as we formalize this activity. As we have groups explain their thinking during the debrief, we frequently will ask other groups to restate what that group said differently or ask other groups who we knew had a different method to explain their idea. A big part of our debrief is to take the communication from individuals in a group, and start spreading ideas across groups so that consolidation can occur.
The Goal of Math Class is BOTH Content and Process
When we teach a math class, the content is definitely important and one of the most obvious things we expect students to take away from the course. However, when students ask “When Am I Ever Going To Use This?”, the best answer may not be when they will use the content. Instead, show them that inside of every lesson are skills they will need every day:
Critical thinking
Creativity
Collaboration
Communication
We are not just setting them up for success if they want to go into a mathematics field, but whatever life throws their way.
Next time you grab any lesson answer key and read through the questions, red, and blue ink, remember that the lessons were designed not just to teach mathematics content, but also skills that they will need every day. Perhaps you’ll find that “When Am I Ever Going To Use This?” is one of the most exciting questions we can answer in our math classrooms.
So what are some specific teacher moves we can make to best support the development of these 4 C's within an EFFL lesson? Read on to part 2 of this series.
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