That’s Not Very Authentic, Now Is It?: Increasing the Level of Authenticity in Math Class

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A while back, I wrote about the need for authenticity in math class.  It’s a truth that all math teachers seem to face at one point or another during their career.  A student voice comes out of the blue: “Why do we need to know this?”  As teachers, we know the answer to this question.  In fact, we know many answers to this question.  Most of the time, we address the question by spewing out the laundry list of different places that you can find that particular concept used in the ‘real world.’  As if to point out something they didn’t already know, we tell them that the word problem shows them one of those places.  If we are lucky, the student responds with a semi-satisfied look and goes back to struggling with the problem— the same problem that they are still not quite sure why they are doing it in the first place.  That’s not very authentic, now is it?  One thing’s for certain: the question will come up again.  If it’s not from the same student, from another.

As educators, we are left to wonder:  if the math that we teach is already written in a context where the skills are applicable, why are our students not making the connection?  It’s analogous to reading a really good book.  The author’s words can paint a picture and make us feel like we are observing the events as they unfold.  But that’s all we will ever be: observers.  When our students are looking at a word problem, that’s all the more they can be: observers.  Just as with reading a good book, they have no ability to influence the outcome.  They cannot be creators and therefore our students do not feel involved in the process.  The best outcome that can be hoped for is that the answer to the problem turns out to be the right one.  Even the best curricular resources that tout their ability to connect the student to a real mathematical context can only go as far as making the students observers of information rather than creators of it.  Can we really be surprised when a student doesn’t make a true connection to the math is being taught?  We are often shocked when a student doesn’t want to complete a problem because it’s too hard.  When a student’s wall goes up, would it not be easier to tear it down if they knew why they were doing it in the first place?

We all recognize the need for what we teach to be relevant to our student’s lives.  Every teacher can tell you the positive results that are experienced when our students see a value in what they are doing.  Even further, when students see themselves as makers of products and creators of information, we awaken a drive in our students that they didn’t even realize was there.  I have watched as each of the other subject areas has become increasingly more authentic while math seems to be stuck in the quasi-authentic trap of ‘real-world’ word problems and math tasks.  If we know the positive impacts that truly authentic teaching can have on our learners, then why aren’t we teaching this way?  What are we waiting for?

Let’s first start by taking a deeper look into the varying levels of authenticity that can exist in our math classroom spaces.  A while back, my co-teacher and I did a small presentation to a group of aspiring math teachers. We were put the task of categorizing the various levels of authenticity.  I will attempt to briefly outline the levels while outlining my experiences with them.

Hierarchy of Authenticity

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Real World Problem Solving: Math Tasks

Most math teaching that claims to be ‘authentic’ exists at this level of authenticity.  We can find the majority of the textbook word problems and tasks in this category.  There is an attempt made for connection, but the learners have no influence on the outcome.

I taught using the Connected Mathematics curriculum for two years.  This program was created in collaboration with the National Science Foundation (NSF) and claimed to be based in application.  In many ways, this curriculum was a model for ways to teach inquiry based mathematics.  It provided an overarching context that was based on where the math would show up in the ‘real-world’, but there was something missing.  The connections that were being made didn’t seem to be relevant to many of the students’ lived experiences. They could see a vague connection as an observer of information, but the connections didn’t take hold.

I worked through some of the lessons and wrote them into the students’ lived experiences by changing names, places, or completely re-writing sections of the book.   By putting familiar people, places and events into the context of the problems our students can more readily relate to the material.  Although there was a significant improvement in the level of engagement, the question still came up.  I wasn’t satisfied with the result.  Although there is nothing wrong with this level of authenticity, I think we can do better.

Culminating Projects: End of Unit Application of Knowledge

IMG_1935When teachers are looking to become a little more authentic with their processes, they tend to use capstone projects to highlight and review the information that was ascertained throughout a unit.  At its highest level of authenticity, the project will honor student interest and speak to their lived experiences.  But that’s not what usually happens.  Too often, these culminating projects have given little consideration to the connection that it provides to the students’ truths.  The culminating project is simply taken from a source— whether it be the many sources that are provided on the internet or from a curricular resource.

Although culminating projects serve an excellent role in allowing students to engage with the content at a deeper level, there is a lot left to be desired when it comes to driving student learning.  Often, students see culminating projects as something that are an add-on to what has already been learned in class.  It lacks the fluidity that reminds the students why they were learning the content in the first place.  During the 2 years that I taught using the Connected Mathematics curriculum, there were a lot of great culminating projects that built upon what was already learned.  I tweaked and adapted in an attempt to make the project more relevant to the student truth.  In short, the majority of students were still not seeing the connection between math and their world.

In the final unit that I taught using the Connected Math curricular model, I decided to go head-on and have the students engage in an experience where the math was truly relevant.  We placed ourselves into the shoes of foresters who were seeking to understand the diversity of tree species in a nearby forest.  We used authentic sampling techniques and delved into equations that forests used to determine species diversity.  This was an outstanding experience for the students, but there was still something missing.

All along the way, I saw in-roads in which we could have used the context in order to drive student learning.  Instead of using the project as a capstone, the essential question could have been used as the vehicle to propel student questions and create the ‘need to know.’  Culminating projects are a great way to teach students by placing students into the context of a problem.  I think we can still do better.

“The Need to Know”: Authentic Experience Guides Teaching

IMG_3625Reflecting on the final culminating project led me to the idea that if we really want students to know something and know it well, we must create the need to know within them.  Using an authentic question or problem to drive the math content learning allows us to draw the students into the context and make it their reality.  They become interpreters, creators and makers.  In every unit experience, the students have assumed the role of an actual profession.  They became geographers, architects, and engineers and were a part of a team producing a final product.  The ability of the team to seek out and interpret new knowledge ultimately impacted the end result.  I will do more to describe this process in future blog post, but for now let’s dig further into the reason we need to step our game.

When we step out into the world that exists beyond the walls of the classroom—into professional realities— we rarely see learning happen for the it’s own sake.  Learning takes a more subject-centered approach.  Professionals gather around a subject and learning happens out of necessity.  People seek new knowledge in pursuit of the answer to a question or the solution to a problem.  During this process, new knowledge is gained in service of the subject.

By focusing on a problem or a question, we can develop the ‘need to know’ in our students and begin to create students who are driven to pursue the information that is necessary to solve the problem or answer the question.  Through flipping the traditional model of learning on its head and taking a more subject-centered approach to teaching, we create two avenues for student success.  First, we are creating the conditions in which students can truly immerse themselves in their learning.  By identifying a problem or a question that relates to the students’ lived experiences we create witIMG_3658hin them a sense of urgency: the need to know.  Additionally, we allow the students to pursue new information and understanding as it relates to the problem that is being solved.  Students are asked to take ownership in effort to make sense of the problem and draw the appropriate conclusions.  In this regard, the students learn how to become independent thinkers and problem solvers.

Using a variety of teaching models and resources, we can allow the students to pursue avenues that cause them to become successful problem solvers and truth seekers.  These are the skills that will carry them into the future and make them more likely to engage in seeking out problems and work to solve them.  All along the way, the students are becoming the drivers of their own learning.

Final Thoughts

If we want our learners to be critical thinkers and problem-solvers that are equipped with the skills necessary for success in the 21st century, why aren’t we teaching students in a way that allows them to become the problem-solvers that we seek?   We no longer exist in a world that allows any one person to be the holder of all knowledge.  Anyone who has access to the internet and a desire to solve a problem can acquire the necessary information with the click of a button.  Shouldn’t our classrooms be set up to honor this reality?  While thinking about the desired outcome, we must focus on the processes that we teach along the way.  Any time that we are able more closely replicate the realities that exist outside of the classroom, we are honoring our students and teaching them the skills needed for success in the this century not the last.

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