Math as Metaphor: Connect Physics-Chemistry-Biology …bioquest.org/wp-content/uploads/2014/02/Connect... · References Uri Treisman, Webcast Jan. 2014 “National Trends in ollegiate

MATH AS METAPHOR: CONNECT PHYSICS-CHEMISTRY-BIOLOGY WITH DEVELOPMENTAL MATH INSTRUCTION

Linda M. Grisham, Massachusetts Bay Community College

[email protected]

math/science gurus:

Claudia Neuhauser

Adebanjo Oriade

Tony Weisstein

met·a·phor (metəˌfôr,-fər/) noun

A thing regarded as representative or symbolic of something else, especially something abstract

Math Dilemma at Open-Access Colleges “.. recent federal data indicate that 68% of community college students and 40% of students at open-access four-year colleges take

at least one remedial course. Research suggests that many more students are referred to developmental courses but never enroll in them…”

“..For instance, among the 63,650 students in the study who were

assigned to three levels of developmental math, only 11 % ever successfully completed college-level introductory algebra. …And even among the students who had the tenacity to complete all three levels of remedial math ~25% of those who completed all three developmental courses) failed to enroll in the gatekeeper math course…”

“…many students assigned to developmental courses drop out before completing their sequence and enrolling in college-level courses..” Taken from “What We Know About Developmental Education Outcomes,” 2014, Community College Research Center.

The math course is envisioned as a 6-hour/week developmental math course that will prepare students for success in pre-calculus (re-envisioned), statistics, freshman chemistry & algebra based physics courses.

Math Proficiency:

• conceptual understanding—comprehension of mathematical

concepts, operations, and relations

• procedural fluency—skill in carrying out procedures, flexibly,

accurately, efficiently, and appropriately

• strategic competence—ability to formulate, represent, and solve

mathematical problems

• adaptive reasoning—capacity for logical thought, reflection,

explanation, and justification

• productive disposition—habitual inclination to see mathematics as

sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

Taken from Adding It Up: Helping Children Learn Mathematics, (2001) National Academies Press.

(Uri Triessman)

Translate Math Equations & Processes!! • Translation Activities: writing out the definitions, examples,

illustrating word problems in pictures and words.

• What do the symbols mean to students? Make sure we are on the

same page. Example 5 = 5 wrong??

• Estimation and sense making • Fractions, per cents, & proportional thinking

• Use algebra, geometry, & statistics physical and virtual

manipulatives for concept exploration and sense-making.

• Concurrent use of ALEKS adaptive software to build math skills. Goal? Move students to a pre-calculus level.

Connect Science Phenomena to Math Use of ST/SD, concept mapping, cycle drawing –develop intuition about graphs generated by math functions or data.

ST/SD systems thinking/systems dynamics modeling: There are many physics, chemistry, biology, environmental, social science, & math interactive models available in ‘run time’ versions.

Predator-Prey Modeling

Observe Science Phenomena, Collect & Analyze Data

iPad for Data Collection and Analysis

Time Spent

Pro

ject

s W

ork

ed O

n

Translate

Math

Equations & Symbols

Achieve

Mastery & Confidence

Working Toward Mastery

Connect

Science, Math

& Data Analysis

References Uri Treisman, Webcast Jan. 2014 “National Trends in Collegiate Mathematics” from AMATYC, https://tgslc.adobeconnect.com/_a824644690/p3r3da2j712/?launcher=false&fcsContent=true&pbMode=normal Uri Treisman & S.A. Surles, (2001), “Systemic Reform and Minority Student High Achievement,” p.260 in The Right Thing to Do, The Smart Thing to Do Enhancing Diversity in the Health Professions, no. 10186 National Academies Press. http://www.nap.edu/download.php?record_id=10186 Report to the President: Engage to Excel: Producing One Million Additional College Graduates with Degrees in Science, Technology, Engineering, and Mathematics (2012), President’s Council of Advisors on Science and Technology http://www.whitehouse.gov/administration/eop/ostp/pcast/docsreports Jeremy Kilpatrick, Jane Swafford, Bradford Findell, Editors, (2001), Adding It Up: Helping Children Learn Mathematics, National Academies Press, no. 9822. http://www.nap.edu/catalog/9822.html

“Resources and Reform: Thinking Through the Costs of a Developmental Math Redesign.” This webinar looks at what college resources are required to implement a statewide redesign of developmental mathematics, drawing on interviews with faculty, administrators, and staff in Virginia community colleges. http://ccrc.tc.columbia.edu/publications/resources-and-reform-developmental-math-redesign.html Davis Jenkins and Sung-Woo Cho, (2014), “Get With the Program ... and Finish It: Building Guided Pathways to Accelerate Student Completion,” working paper no. 66, Community College Research Center. http://ccrc.tc.columbia.edu/publications/get-with-the-program-finish-it.html Nikki Edgecombe, (2011), “Accelerating the Academic Achievement of Students Referred to Developmental Education,” working paper no. 30, Community College Research Center. http://ccrc.tc.columbia.edu/publications/accelerating-academic-achievement-developmental-education.html Elisa Rassen, Priyadarshini Chaplot, David Jenkins, and & Robert Johnstone, (2013), “Nuances of Completion: Improving Student Outcomes by Unpacking the Numbers,” Community College Research Center. http://ccrc.tc.columbia.edu/publications/nuances-completion-student-outcomes-cbd.html

Resources ALEKS, http://www.aleks.com/ (McGraw-Hill) Assessment and LEarning in Knowledge Spaces is a web-based, artificially intelligent assessment and learning system, available online 24/7. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. ALEKS then instructs the student on the topics she is most ready to learn. As a student works through a course, ALEKS periodically reassesses the student to ensure that topics learned are also retained. ALEKS courses are very complete in their topic coverage and ALEKS avoids multiple-choice questions. http://www.aleks.com/highered/math/research_behind_aleks “Changing Paradigms,” animated TED Talk by Sir Ken Robinson generates thoughtful student discussions on the need for active teaching/learning pedagogies. http://youtu.be/zDZFcDGpL4U ALPS Program (Accelerated Learning Program) at the Community College of Baltimore County. http://alp-deved.org/ Math Words http://www.mathwords.com/ An interactive math dictionary with enough math words, math terms, math formulas, pictures, diagrams, tables, and examples.

Shodor Foundation, nonprofit organization serving students and educators by providing materials, models, and instruction relating to computational science (scientific, interactive computing) http://shodor.org/ Maryland Virtual High School of Mathematics and Science (maintained by the Shodor Foundation) is repository of mostly system thinking/dynamics models for biology, chemistry, physics, earth/space science, environmental science and math. http://mvhs.shodor.org/ InterActivate (engaging, interactive math and science exploration activities) Shodor Foundation Inc., http://www.shodor.org/interactivate/ Creative Learning Exchange, has an extensive library of systems thinking/dynamic models, lessons (STEM, social science & humanities), and tutorials http://www.clexchange.org/ System Thinking in Schools (K-12), The Waters Foundation http://watersfoundation.org/our-resources/ Vernier Video Physics App for iPAD, iPhone, & iPod Touch records and analyzes video motion clips. http://www.vernier.com/products/software/video-physics/

iSee Systems. Inc., dynamic (and expensive) systems thinking/dynamics software (STELLA & iTHINK). http://www.iseesystems.com/ Vensim by Ventana, system thinking/dynamics software, free to download from http://vensim.com/free-download/ for use by students and educators. Teaching Algebra with Manipulatives, Glencoe/McGraw-Hill, Columbus OH, sault.eup.k12.mi.us/cms/lib/MI17000143/Centricity/Domain/137/a2tam.pdf Teach Mathematics: Algebra Virtual Manipulatives http://www.teachmathematics.net/page/2958/algebra-virtual-manipulatives Teach Mathematics: Geometry Virtual Manipulatives, http://www.teachmathematics.net/page/2960/geometry-virtual-manipulatives Teach Mathematics: Statistics Virtual Manipulative, http://www.teachmathematics.net/page/2961/statistics-virtual-manipulatives Science Case Net, repository of problem based learning cases and a network for educators http://sciencecasenet.org/ PBL Clearing House, repository of problem based learning cases at University of Delaware. http://www.udel.edu/inst/