The document discusses how traditional math curriculums fail to teach students how to apply mathematical concepts to real-world contexts. It argues that the root cause is a lack of emphasis on contextual or applied math education. The solution proposed is for math courses to integrate real-life problems and applications to help students understand how mathematical tools can clarify practical situations.

1. MATH AND BIOTECHNOLOGY
Conference on Integrating Workforce
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Development into Curricula
Miramar College
January, 2012
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Lisa Seidman

2. Handout
Hando t
• Resources on handout
• Other ideas?

3. What’s the Problem?
• Many students struggle with laboratory
calculations, e.g.
– Setting up dilutions
– Preparing solutions to a particular molarity
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4. • In a workplace, their errors can have serious
consequences
• In a college, can result in student failure,
attrition, slowing the p of classes
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5. So…
So
• Most teachers/programs help students with
calculations
– Separate courses
– Modules
– As portion of laboratory courses
– As part o “bridge” p og a
s pa of b dge program
– Etc.

6. ROOT CAUSE
• Learn from the quality experts that it is not
enough to identify problem
• Not enough to solve a problem
• Need to identify and fix root cause – otherwise
problem is likely to recur

7. Tend to Think Root Cause is Lack of
Math Skill
• But actual math required to do most
calculations is within ability of average
students
• Most students can do math calculations
through basic algebra
• Their problem is language and context

8. This Means
• Root problem is not really math deficit
• Therefore, our contextual laboratory math course is
NOT remedial or d l
di l developmental math
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• Almost every student, regardless of background,
benefits from instruction in biotechnology math
– This includes students with Bachelor’s degrees
– Students with calculus background
– For this reason, we require laboratory math course for all
students, even post-bacs and students who have had
calculus

9. So,
So Is there a Problem?
• Yes, an even BIGGER Problem
• Students cannot solve problems in any practical context
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• Not just biotech
– Health professions
– IT
– Trades
– Business
– Etc.
Etc
• Therefore, all have specialty math courses that are contextual

11. Why
Wh this Problem?
• Maybe the root problem is that the academic
community does not value contextual math
• Such math is considered to be
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“developmental”
• Therefore our students have not learned to
apply the tools they learn in math classes

13. Common Core Math Standards
• We can see this reflected in the standards
• Adopted by 40 states
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14. Measurements and Data– Finished by
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Grade 5
• Measure lengths indirectly and by iterating length units.
• Represent and interpret data.
• Measure and estimate lengths in standard units.
• S l problems involving measurement and
Solve bl i l i d
estimation of intervals of time, liquid volumes, and
masses of objects.
• Geometric measurement: understand concepts of area and relate area to
multiplication and to addition
• Convert like measurement units within a given
measurement system.
• Geometric measurement: understand concepts of volume and relate volume
to multiplication and to addition.

15. Algebraic Expressions and Equations
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by Grade 8
• Reason about and solve one-variable equations and
inequalities.
• Represent and analyze quantitative relationships between
dependent and i d
d d d independent variables.
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• Use properties of operations to generate equivalent
expressions.
• Solve real-life and mathematical problems using numerical
and algebraic expressions and equations.
• Understand the connections between proportional
relationships, lines, and linear equations.
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• Analyze and solve linear equations and pairs simultaneous
linear equations.

16. • According to standards, by grade 8, have
learned almost all math tools needed for
majority of occupations
• But do they ever learn how to use them?
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17. What are They Learning in High
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School?
• A-APR.2. Know and apply the Remainder
Theorem: For a polynomial p(x) and a number
a, the remainder on division by x – a is p(a),
so p(a) = 0 if and only if (x – a) is a factor of
p(x).

18. • A-APR.3. Identify zeros of polynomials when
suitable factorizations are available, and use
the zeros to construct a rough graph of the
function defined by the polynomial.

19. • Use polynomial identities to solve problems.
• A-APR.4. Prove polynomial identities and use them to
d ib numerical relationships. F example, the
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polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2
can be used to generate Pythagorean triples.
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• A-APR.5. (+) Know and apply the Binomial Theorem
for the expansion of (x + y)n in powers of x and y for
a positive integer n, where x and y are any numbers,
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with coefficients determined for example by Pascal’s
Triangle.1

20. What Does this Mean for Us?
• We need to teach contextual math as a part of
our curriculum
• In the bigger picture, as educators???

21. Sol Garfunkel and David Mumford
Op Ed in NYT
“How often do most adults encounter a situation in
which they need to solve a quadratic equation? Do
they need to know what constitutes a ‘group of
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transformations’ or a complex number?...A math
curriculum that focused on real-life problems would
s e pose s ude s o e abs ac oo s of
still expose students to the abstract tools o
mathematics…But there is a world of difference
between teaching ‘pure’ math, with no context, and
teaching relevant problems that would lead students
to understand how a mathematical formula…clarifies
real-world situations.”

22. They Concl de With:
The Conclude With
“It is through real-life applications that
mathematics emerged in the past, has
flourished for centuries, and connects to our
culture now.”