News from Mathnasium of Lakewood
Tutor or Instructor
Aug 13, 2015
What are your goals for your student? Are you looking to help them get through one assignment? Are you looking to help them pass one test? Or is your goal to help them achieve true mastery and long term success? This article written by Nicholas Mele tells the story of two similar students that chose different solutions when they met struggles in class. Which would you choose for your student?
The Tutor Paradox
Johnny has begun to struggle in math class. His parents recognize how important math is and hire a tutor to help him with his homework. Johnny meets his tutor twice a week and enjoys the help he gets. His homework grades immediately improve and his parents feel better about his performance in class.
Jane has also begun to struggle in math class. Her parents, like Johnny’s, recognize the immediacy of the problem and hire a different tutor for Jane. Jane’s homework grades improve slightly, but her parents wonder why the tutor continues to focus on material Jane has seen in previous years.
A few weeks go by and Johnny sits for an exam on the material on which he and his tutor have been working. Johnny looks at the exam and recognizes some of the problems but struggles with others he does not recognize. He completes the exam and returns home eager to learn his results. He and his parents are surprised when his grade is no higher than those on his previous exams. Johnny and his parents are left wondering what went wrong.
Jane sits for the same exam and, while the material is still challenging for her, Jane completes the exam and scores a bit higher than she had on previous exams.
After a few months of continued work with their respective tutors, Johnny continues to score poorly on his tests but Jane’s scores have consistently improved and she finds herself needing less help on her daily homework.
So, what’s the difference between Johnny and Jane?
Johnny experienced what many students experience who have relied on tutors for homework help. The cycle of high homework grades but low test grades is all too common in math classes. Unfortunately, having a tutor focus on homework help tends to create and perpetuate this cycle with students. In fact, it is not uncommon for math teachers to base homework grades mainly on completion, rather than on accuracy. Even if Johnny’s teacher graded his homework for accuracy, it is likely the grades would be inflated by his tutor’s assistance and indicate a higher level of understanding than Johnny had actually attained.
When students begin struggling in math classes, it is easy to think the material they are seeing is too complex and the classroom time or instruction is deficient. Traditionally, this has been remedied by offering extra instruction time, often with a tutor focused on the same material. Quite often, however, this is not actually the cause. Usually, the inability for a student to understand the classroom material is a symptom of a larger issue: a weak foundation and a lack of fundamental skills. When students set aside extra homework time only in an attempt to complete the homework, especially with a tutor, they are treating the symptom and not the root of the problem… and the problem will persist. Recent studies have shown that students involved in these types of traditional tutoring programs show very little growth or improvement.
Mathematics, perhaps more than any other subject in primary and secondary grades, is highly foundational and linear in its design. The mastery of prerequisite skills is absolutely essential in order to move forward and fully understand any additional concepts which build upon those prerequisites. When children develop gaps in their mathematical foundation, they will struggle down the road. When specific steps are not taken to address those gaps, the gaps will grow larger and the struggles will continue and likely worsen.
For students with these kinds of struggles, the solution is simple but not easy. The foundational gaps
must first be identified. Curriculum then needs to be generated to address those identified gaps. And
finally, the student must be provided good instruction to close the gaps. Most classroom teachers
would love the opportunity to provide this solution, but simply have neither the time nor the resources
to do so. So the task falls to the parents to find a supplemental education source. Jane experienced
success with her tutor because her parents chose an option which provided these three essential parts
to improving her understanding of math:
1) A diagnostic instrument designed to identify Jane’s weaknesses and gaps in her foundation
2) Curriculum designed to remediate those weaknesses
3) A good instructor to teach Jane the math she had been missing
Jane’s instructor identified areas and concepts Jane might have seen, but had not mastered. She chose
materials best suited to remediate those concepts and she taught Jane well.
The fundamental difference between Johnny’s tutor and Jane’s instructor is what drives the interaction
with the student. Johnny’s interaction is driven by the material Johnny is faced with in class. His tutor
used Johnny’s homework as a guide to instruction. The problem is that Johnny may not have the proper
foundation to understand the material he is facing in school. This “mismatch” in Johnny’s level of
understanding and the level of his homework puts success in the class out of reach. Focusing attention
on the homework will not fix this mismatch and Johnny will continue to struggle.
Jane’s interaction, however, was driven by her own mathematics background. Jane’s instructor chose a
curriculum based on Jane as an individual. Jane’s instructor approached Jane at her own level of
understanding and specifically worked on eliminating the mismatch between her understanding and her
homework. This kind of targeted instruction has dramatic and long term benefits. According to a report
by the National Bureau for Economic Research released in 2014, effects of targeted instruction “…are
larger – much larger – than what we see from so many other educational strategies.” (Ludwig, 2014)
The approach used by Jane’s instructor is a long term approach to solving a long term problem. These
foundational gaps do not occur overnight. In fact, they are sometimes years in the making and often
require an extended solution. As Jane’s fundamental understanding of math increases, she will be
better able to understand the concepts she faces in her class. Ultimately, the goal for Jane is to develop
the ability to efficiently internalize classroom material and eliminate the need for homework help. This
approach is far more effective than a traditional tutoring approach and will have a powerful and long
lasting positive impact on the student. It can transform the way a student sees math and how he or she
feels in a math class. Jane might even begin to enjoy math class.
By Nicholas Mele
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