[RUME] Blanking on Tests

[Jerome Epstein]

I would submit that math anxiety is often (I don't know how often) the 
same phenomenon. They solve homework problems by "pattern matching" and 
do not undertstand anything. Then if they cannot pattern match on the 
test they are helpless. I have seen it a thousand times. We have so many 
students at Polytechnic who have passed a caclulus course in high 
school, with decent grades, and cannot function with the questions on an 
8th grade review book. My department head could tell you stories. . . . . .
Jerry Epstein

Metronym wrote:

>  Andy brings up an important topic.  Students can "blank on tests" for two
>reasons.  The first is probably the more common - they have watched you do
>the problems, they can follow the model to do the homework, they can retain
>the model long enough to accomplish a quiz but they do not retain nor do
>they know the material.  The second is a more serious reason.  They may
>suffer from math anxiety.  I will adress both problems.  The "cure" is
>similar in both cases.
>  In the case of the first problem, the student simply lacks concentrated
>practice.  Often, the student voices, "I understood everything you did in
>class, but I just blanked when I did the homework, quiz, etc."  Many of our
>students come to college without study skills for mathematics.  High schools
>very typically teach on short term topics.  High schools textbooks further
>this problem.  It is the it-must-be-Tuesday-because-we-are-doing-logarithms
>connundrum.  First of all, students better retain material if it is always
>joined with other content.  On the college level, we are not particularly
>teaching algebra, logarithms, trigonometry, or whatever in our approach to
>Calculus.  However, the student must have those tools polished and at the
>ready each day of study.  Placing tools within context often helps that
>problem.  Secondly, in some high schools, the student grows accustomed to
>learning a skill for the test and then dropping it in favor of the next
>skill.  They do not learn how to study comprehensively.  They learn one
>trick and then are tested on one trick.
>  I recommend that all of my students, approximately 4 days before a
>preliminary examination (7 days for a midterm or final) read their notes,
>highlighting any detail that does not immediately bore them with its
>familiarity.  They are then asked to transcribe each of the highlighted
>topics onto a piece of paper with sufficient detail to understand each facet
>of concern.  Needless to say, this is the appropriate time for the student
>to conference with the instructor if additional understanding is needed.  In
>the meantime, they are asked to formulate their own sample test:  10-15
>questions (depending on the material) that are culled from their notes,
>homework and/or quizzes.  These problems should be the ones that offer them,
>individually, the most challenge and/or trouble.  I will return to this
>strand of thought after a few comments about math anxiety.
>  Math anxiety is a pervasive problem.  There are multiple research papers
>that explore this very real difficulty.  Suffice it to say, students who
>suffer with this are not learning-disabled but rather, at some point,
>subject to poor teaching for their particular learning style.  The typical
>story is about the second grade teacher who decides to present an enrichment
>activity to her class.  She challenges them with three rows of three dots,
>comprising a nine-dot square and asks them if they can connect all nine dots
>with four straight line segments without ever lifting their pencil.  The
>next day, the children rreturn and one child, let's say Johnny, proudly
>announces he can do it.  He is invited to the board where nine dots are
>awaiting his efforts.  After successfully connecting the dots, he is praised
>in front of his classmates for his cleverness.  In the meantime, Susie, in
>the back of the room, raises her hand and says she can connect the dots, but
>she did it a different way.  The teacher, perfectly aware there is only one
>way for solution (the first problem) invites Susie to the front of the room
>for failure in front of her classmates.  The teacher redraws the nine dots
>on the board, but Susie says she cannot do it on the board and aks for the
>paper easel to demonstrate her solution.  Faced with the nine dots now
>available for her on the paper, she folds the paper, and carefully connects
>the dots.  The teacher says that Susie is wrong.  Susie objects, stating
>that the teacher never said "you can't fold the paper."  Susie returns to
>her seat, having learned a very valuable lesson.  Stifle creativity and wait
>for the "right" answer.  Otherwise, you can end up humiliated in front of
>your friends.
>  If you pair that sort of experience with one similar to my following
>observation, you observe math anxiety in the student.  During a two-year
>hiatus from my graduate work, I taught in a high school.  A new hire
>appeared on the scene, famous for her discipline and keeping students after
>school.  One afternoon, needing to use the computer that was available in
>the back of the classroom, I observed this new hire lecturing her
>imprisoned-after-hours students.  she wrote a third degree polynomial on the
>board, setting it to zero.  She moved the constant to the other side of the
>equation, factored an 'x' out of the remaining terms, factored the resulting
>quadratic and then set each of those factors equal to zero.  One of the
>prisoners was awake enough to query how zero could equal that isolated
>constant on the other side of the equation.  At this point, I expected her
>to erase her work, apologize (or mutter that covering phrase "I just wanted
>to see if you were paying attention...") and correct her work.  She did not.
>After erasing the final answer, but leaving the entire development on the
>board, she said, "Well, those answers are wrong but it is your job to find a
>number such that (sic) 'x' times 'x + 5' times 'x ­ 2' equals 7."  I sat in
>the back of the room thinking, "Even God could not do that.  That's the
>reason we have the rational root theorem."  Two days later, her class of 29
>pre-calculus students all failed her exam.  And she had just mounted a
>horrendous achievement.  Left in her wake were 29 high school juniors and
>seniors who honestly believed that they could not do math - that it made no
>sense.
>  Query those students that you may suspect are suffering from math anxiety.
>In my own experience, every single one of them will tell you of the time
>that math no longer was rewarding, logical or sensible.  Convinced they
>cannot succeed, they suffer terrible anxiety under testing situations even
>in a new venue, with excellent instruction.
>  As I mentioned, in both cases, ask them to go through their notes,
>codifying all topics of interest for study as well as forming a sample test
>based on the problems they find the most challenging.  Each day, prior to
>the exam, the list of topics should shrink in size but not in number, until
>the night before the test, they have a small notecard that brings immediate
>recall of each area.  In the  meantime, they should take their sample test
>at least twice daily.  For those students with math anxiety, they should
>take the test five times in a row the night before the exam.  They will hate
>doing this, because it seems like busy work, but the repetition will imbue
>them with a rhythm, a drumbeat of performance, that will tide them over when
>faced with the actual exam.
>  In addition, I warn them that if, during the examination procedure, they
>start to feel that "bubble" of anxiety rising in their throats, they are to
>put their pencil down, look at the clock or some other inanimate object,
>take a deep chest breath or two and relax their shoulders and neck before
>resuming the test. 
>  It is a shame that these students are paralyzed to act during an
>examination due to past poor instruction, but we must deal with our
>students, one at a time, as they come to us to effect meaningful learning.
>  For those students who simply do not know how to study, the techniques
>mentioned will give them a structure for studying and improve their
>performance.
>  Some students are so badly injured that they may need to be reminded often
>about these techniques with requisite reassurance in order to improve their
>performance.  Those students who do not need this attention are not
>necessarily brighter or more capable.  They simply have the good luck of
>past instruction that was appropriate and meaningful for them.  Let us know
>how your students fare!
>
>Regards,
>Alden
>Alden L. Monberg, PhD
>Applied Mathematics and Coastal Processes
>Maine Maritime Academy
>amonberg at mma.edu
>http://www.monbergmath.com  
>
>
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