Presentation9 lab math seidman

MATH AND BIOTECHNOLOGY

Conference on Integrating Workforce g gDevelopment into Curricula

Miramar CollegeJanuary, 2012y

Lisa Seidman

Hando tHandout

• Resources on handout• Other ideas?

What’s the Problem?What’s the Problem?

• Many students struggle with laboratory calculations, e.g.– Setting up dilutions– Preparing solutions to a particular molarityp g p y

• In a workplace, their errors can have serious consequences

• In a college, can result in student failure, attrition, slowing the pace of classes, g p

SoSo…

• Most teachers/programs help students with calculations– Separate courses– Modules– As portion of laboratory courses– As part of “bridge” programs pa o b dge p og a– Etc.

ROOT CAUSEROOT 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 • Need to identify and fix root cause – otherwise

problem is likely to recur

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• Their problem is language and context

This MeansThis Means

• Root problem is not really math deficit• Therefore, our contextual laboratory math course is

NOT di l d l t l thNOT remedial or developmental math• Almost every student, regardless of background,

benefits from instruction in biotechnology mathbenefits 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

So Is there a Problem?So, Is there a Problem?

• Yes, an even BIGGER Problem

• Students cannot solve problems in any practical contextp y p• Not just biotech

– Health professions– IT– IT– Trades– Business

Etc– Etc.

• Therefore, all have specialty math courses that are contextual

Wh this Problem?Why this Problem?

• Maybe the root problem is that the academic community does not value contextual math

• Such math is considered to be “developmental”p

• Therefore our students have not learned to apply the tools they learn in math classes apply the tools they learn in math classes

Common Core Math StandardsCommon Core Math Standards

• We can see this reflected in the standards• Adopted by 40 statesp y

Measurements and Data– Finished by yGrade 5

• Measure lengths indirectly and by iterating length units.• Represent and interpret data.• Measure and estimate lengths in standard units.

S l bl i l i d • Solve problems involving measurement and 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.

Algebraic Expressions and Equations g p qby Grade 8

• Reason about and solve one-variable equations and inequalities.

• Represent and analyze quantitative relationships between d d d i d d i bldependent and independent variables.

• 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 l h l d lrelationships, lines, and linear equations.

• Analyze and solve linear equations and pairs simultaneous linear equations.

• 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?y

What are They Learning in High y g gSchool?

• 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).

• 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.

• Use polynomial identities to solve problems.• A-APR.4. Prove polynomial identities and use them to

d ib i l l ti hi F l th describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples.g y g p

• A-APR.5. (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for i i i h d b a positive integer n, where x and y are any numbers,

with coefficients determined for example by Pascal’s Triangle.1 Triangle.1

What Does this Mean for Us?What Does this Mean for Us?

• We need to teach contextual math as a part of our curriculum

• In the bigger picture, as educators???

Sol Garfunkel and David MumfordOp 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 y g ptransformations’ or a complex number?...A math curriculum that focused on real-life problems would still expose students to the abstract tools of s e pose s ude s o e abs ac oo s o mathematics…But there is a world of difference between teaching ‘pure’ math, with no context, and teaching relevant problems that would lead students teaching relevant problems that would lead students to understand how a mathematical formula…clarifies real-world situations.”

The Concl de WithThey Conclude With:

“It is through real-life applications that mathematics emerged in the past, has flourished for centuries, and connects to our culture now.”