Bridging the Gappeople.stfx.ca/rlukeman/talk.pdf · Bridging the Gap Reflections on First-Year...
Transcript of Bridging the Gappeople.stfx.ca/rlukeman/talk.pdf · Bridging the Gap Reflections on First-Year...
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Bridging the GapReflections on First-Year University Calculus
Ryan Lukeman,Dept. Mathematics, Statistics, and CS
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Introduction
• B.Sc., StFX 2003, M.Sc., Dal 2005, Ph.D UBC 2009, prof @ StFX 2009-present
• Taught calculus at both UBC and StFX
• Taught calculus every year (3 times with double sections) at StFX
• Dept. Coordinator for Calculus since 2010
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The state of calculus and
calculus studentsin university
Pinpointing challenges
Collaborative motivationof students
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Stewart’s Calculus Book is used by over 70% of the first-year market in North America
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Typical Evaluation
• Weekly quiz based on homework (15%)
• One-hour per week lab component using Maple (10%)
• Midterms (30%)
• Final (45%)
• class sizes: 45-70 students at StFX, class averages: around 60%-70%
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These students areterrible. Do they learnanything in high school?
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These students areterrible. Do they learnanything in high school?
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trigonometry*geometry(
algebra'
arithme(c*coun%ng'
."what"we"studied"last""class"
what%we’re%studying%today%.%
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Identifying a problem at X
• 2010-2013, increasing problem with student retention in first-term calculus (peaking in 2012)
• 2012-2013: initiated review of calculus course
• Changed text, syllabus, introduced diagnostic component (pre-calc), removed 3 class review of precalculus, extra midterm
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enter university
t
early diagnostic
andintervention
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Digging Deeper
• What did you take in High School?
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Observations
• By and large, students with HS calculus adequately prepared for Calculus I.
• problems at university level stem from:
• complacency, delay in identifying gaps in knowledge
• the background they enter with
• time away from math
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Male vs. Female Performance
Female students on average consistently outperform male students by 5-7% in first-term calculus
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Possible gender factors
• Talented male students disproportionately enter engineering versus females
• Delayed versus instant gratification
• Higher prevalence in males of over-confidence due to taking high school calculus
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enter university
t
opportunity totake calculusat HS level
early diagnostic
andintervention
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The ‘Good High School Teacher’ Effect: An Example
• In 2011, I noticed that students from Dr. J. H. Gillis Regional (local school) were performing very well.
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opportunity totake calculusat HS level enter university
t
effectivehigh schoolinstructor
early diagnostic
andintervention
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The state of the university calculus class:Questions?
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Specific challenges
• Overwhelmingly, students struggle with mechanics of performing calculus, not concepts of calculus.
• Algebra, algebra, algebra.
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The nefarious trio
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Canceling everything in sight
Being cheap with parentheses
And a host of others...
http://www.calvin.edu/~scofield/courses/materials/tae/
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Getting the student ready
• Over a decade ago, regional mathematics professors convened to create a calculus readiness document for entering students.
http://cs.smu.ca/apics/calculus/CalcPrep1.pdf
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.
.
.
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An example
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• difficulty I: making functions work for you
versus...
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(run) (swim)
-comfort converting radical and exponent form-need to know there’s a friendlier form
for the algebraic solution down the road
-need to have a toolbox of available manipulations-cross-multiplying percolates up as
reasonable way to rewrite
(pythagorean theorem)
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-(avoid trap of x + 50 = 2x)-consider squaring both sides as the logical next step
straightforward algebra to see the problem out
(discard the nonsensical negative root)
After testing endpoints [0,100] via global optimization in function T(x), we find...
(it will take about T(28.86) = 46.65 sec)
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Inability to comfortably work with algebraundermines confidence to work out problems,
prevents the communication of understood mathematics, and isolates the student from
the profoundness of mathematics.
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effectivehigh schoolinstructor
opportunity totake calculusat HS level enter university
t
early diagnostic
andintervention
algebraboot camp
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How do we define success forstudents in first-year calculus?
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Motivating the Math
• Apart from ability, interest in mathematics is very rare for entering calculus students.
• 2/124 listed it as their likely major (September, 2014)
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• Expose students as early and often as possible to
• relatable, ‘uncooked’ applications
• the world of research mathematics
• not nearly as esoteric as it’s made out to be
Motivating the Math
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https://plus.maths.org/content/
Method 1: Online Resources
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• details often not needed - just want to inspire curiosity, purpose, relevance
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Method II: Connecting to Math Researchers
• Most university math departments in the region care deeply about outreach to high schools
• Encourage students to consider mathematics as a potential major
• Traditionally difficult access: schools avoiding university sales-pitches
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effectivehigh schoolinstructor
opportunity totake calculusat HS level enter university
t
early diagnostic
andintervention
algebraboot camp
motivation by excitement
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Thank you for your time.Questions?