MATH AND BIOTECHNOLOGY Conference on Integrating Workforce g g Development into Curricula Miramar College January, 2012 y Lisa Seidman
Handout Hando t• Resources on handout• Other ideas?
What’s the Problem?• Many students struggle with laboratory calculations, e.g. – Setting up dilutions – Preparing solutions to a particular molarity p g p y
• In a workplace, their errors can have serious consequences• In a college, can result in student failure, attrition, slowing the p of classes , g pace
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.
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
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
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 t l th• 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
So, So Is there a Problem?• Yes, an even BIGGER Problem• Students cannot solve problems in any practical context p yp• Not just biotech – Health professions – IT – Trades – Business – Etc. Etc• Therefore, all have specialty math courses that are contextual
Why Wh this Problem?• Maybe the root problem is that the academic community does not value contextual math• Such math is considered to be p “developmental”• Therefore our students have not learned to apply the tools they learn in math classes
Common Core Math Standards• We can see this reflected in the standards• Adopted by 40 states p y
Measurements and Data– Finished by y 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.
Algebraic Expressions and Equations g p q 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. d i bl• 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. l h l dl• 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 g 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).
• 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 numerical relationships. F example, the describe i l l ti hi For l th 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 a positive integer n, where x and y are any numbers, ii i h d b with coefficients determined for example by Pascal’s Triangle.1
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 Mumford Op Ed in NYT“How often do most adults encounter a situation inwhich they need to solve a quadratic equation? Dothey need to know what constitutes a ‘group of y g ptransformations’ or a complex number?...A mathcurriculum that focused on real-life problems woulds e pose s ude s o e abs ac oo s ofstill expose students to the abstract tools omathematics…But there is a world of differencebetween teaching ‘pure’ math, with no context, andteaching relevant problems that would lead studentsto understand how a mathematical formula…clarifiesreal-world situations.”
They Concl de With: The Conclude With“It is through real-life applications thatmathematics emerged in the past, hasflourished for centuries, and connects to ourculture now.”