The Dangers of Independent Math Work

As a product of growing up in the 1980s, I’m surprised that I’m not more paranoid than I currently am.  It was a decade filled with horrors and dangers, or at least that’s what I was lead to believe.  My parents taught me not to talk to strangers as they just want to kidnap you, stay away from white vans as those are the vehicles kidnappers use, don’t use lick and stick tattoos as they are filled with LSD, and don’t eat unwrapped Halloween candy as it is filled with razor blades.  To this day, I still get chills when I see a white van.  Although nothing awful or atrocious ever happened to me or any of my friends or family members, the dangers were real, my parents would tell me.  These things could happen to me, I always thought, and so I lived my childhood and young adulthood in a constant state of fear.  Heck, even as an adult, I’m a very nervous Nelly, always thinking that the worst will happen.  The dangers are lurking just around the corner, I know it.

While I try to keep my crazy paranoia and worry out of the classroom, occasionally I see glimpses of happenings that do harken me back to my dangerous childhood.  Well, that might be a bit of an overstatement, but my nervous past does allow me the opportunity to plan ahead and foresee danger or other negative outcomes.  I’ve gotten very good at thinking through all of the problems that could arise from certain activities or lessons and so when I finalize lessons, units, or activities, they generally are free of the hiccups that some teachers run into in the classroom: Not enough time, too much time, students aren’t engaged, or classroom organization causes problems, to name a few.  Typically, planning for instruction in the classroom is my jam.  I love thinking about all of the what ifs and possibilities.  Being a bit of a worrisome individual helps me to think about all of the ways a lesson or activity could fail or go awry.

Therefore, when I planned my most recent STEM unit, I was very thoughtful in how I arranged the math component of the unit.  As I wanted to provide the students with a bit more choice and freedom in how they work and showcase their understanding of the math objectives covered, I created two options for how they could complete the math work in class.  After they completed a pretest at the start of the unit, they were placed into one of three tracks based on their performance on the pre-assessment.  From there, they could choose to participate in a mini-lesson taught by my co-teacher or I before beginning the assigned set of problems they would need to finish for homework.  During the mini-lesson, the concepts covered in the practice problems are explained, modeled, and reviewed.  The students also have the chance to ask my co-teacher or I any questions regarding what they will need to do for homework.  These mini-lessons range in time but usually last no more than 15-20 minutes in length.  Once the mini-lesson is finished, they return to their workspace in the classroom and start the homework.  If they need help or support while they work, they must ask two peers from their assigned group before seeking help from my co-teacher or I.  We utilized this same method of math instruction earlier in the year and so the students are very familiar with it.   Two to four students from the lower two math groups generally choose this option when working in STEM class on the math component of the unit.   The second option offers the students a bit more freedom and independence.  Rather than sitting through a mini-lesson that they might not need, those students who feel a bit more advanced when it comes to their math skills can choose to fly solo.  They do need to, however, watch a pertinent and relevant video resource and read the assigned introductory pages in their math textbook before beginning the assigned set of homework problems.  This way, they are sure to know and understand the skill they are practicing for homework.  If they have questions while they work, they may seek help from peers in their assigned math group.  We introduced this second option for the math component of this unit to prepare the students for the teaching styles of some of the seventh grade math teachers at our school.  They make use of a blended learning or flipped classroom approach to help the students better own their learning.

While this second option has been more engaging for the students who chose it and has allowed them to work at their own pace, it has also created some challenges that we saw first hand in the classroom today.  We begin every math work period with a check-in assessment regarding skills covered from the previous class period.  The students complete 5-10 problems that make use of the skill they had practiced in class the previous day.  It’s an easy way to formatively assess the students on their understanding of the math objectives covered.  What we found today is that those students who chose the more independent second option for working during the math work periods, struggled to answer questions regarding the specific math vocabulary terms covered.  While they could easily apply the skills learned to complete math problems, they could not define or explain the vocabulary terms.  The students who chose to participate in a mini-lesson prior to completing the homework problems, easily completed this portion of the assessment.

So, the question, of course, is, why did this happen?  Why were the students who were working independently unable to define the math vocabulary terms?  When I asked those struggling students, after they turned in their check-in assessment, if they had watched the assigned video or read the assigned pages in their math textbook before beginning the homework, they all responded, “No.”  Despite being able to simplify algebraic terms and expressions and solve linear equations, they could not explain why subtraction is different from addition or what the difference between consistent and inconsistent linear equations is.  They didn’t take the time needed to fully comprehend the skill and associated vocabulary terms.  While independent work definitely has its positive benefits, it also has a few drawbacks.  The students jump headfirst into solving problems rather than previewing sample problems or understanding the vocabulary words affiliated with the skill covered.

At the close of class today, I made sure to mention this incident to the class and asked them what could be done to prevent this outcome from happening again.  The funny part is, that they all seemed to know what they should do, but they just aren’t doing it.  Perhaps this teachable moment will help those students who choose to work independently to do so more thoroughly and carefully in the future.  I’m curious to see the results of our next check-in assessment.  Will they be able to define and explain the associated math vocabulary terms, or will they still have no clue because they rushed through the required foundation-building pre-work?


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