Math Pathways: What Can Other Fields Teach Us About Essential Math Skills? Lisa Reynolds, PhD Higher Education Coordinating Commission Office of Community Colleges and Workforce Development November 13, 2015 For Hawai’i P-20 Partnerships for Education 2015 Math Summit: Math Pathways and Transitions

CONTEXTUAL BACKGROUND “Ancient History” 2009 Customary Sequence and Common Practices in mathematics Core to College: Mathematics Advisory Committee, Developmental Education Redesign work, beginning 2013 HB 2979: Common Course Numbering, Equivalencies and Outcomes: 2013 workgroup and report

PROJECT BACKGROUND Joint Boards Articulation Committee Math Pathways Collaboration Team proposal to HECC: 2014 Statewide Math Pathways Convening: February 2015 Change in statewide transfer degree requirement: May

MATH PATHWAYS CONVENING FEBRUARY 4, 2015 Purpose: Convene faculty from math + other quantitative disciplines Results: Student responses to “Which math course and why?” Kinds of math judged most and least important Examples of disciplinary problems and exercises that require math 4

5 INTERMEDIATE ALGEBRA STUDENT SURVEY: Which math course and why?

WHICH MATH COURSE AND WHY? Administered via Survey Monkey in November 2014 through mathematics department chairs and instructors 580 total respondents from community colleges and universities across Oregon Primary goal of the survey was to gain student perspective/insight on: Prior coursetaking/ history with mathematics Factors leading to enrollment in Math 95 Ultimate mathematics course and undergraduate degree intentions 6

STUDENT SURVEY: ALL RESPONDENTS- DEGREE GOALS 7

DEGREE GOAL IF ULTIMATE MATH COURSE IS… 8 College AlgebraStatisticsMath 105Calculus

STUDENT SURVEY: ALL RESPONDENTS- MATH GOALS 9

MATH GOALS IF DEGREE SOUGHT IS… CTE Degree or Certif.AGS AAOT AS or ASOT-Business

MATH GOALS IF DEGREE SOUGHT IS A BACHELOR’S DEGREE IN… Natural Sciences Social Sciences Arts & Letters/HumanitiesUndecided

12 FACULTY SURVEY: Most- and Least Important Math?

MOST- AND LEAST- IMPORTANT MATH? Faculty participant survey using specific math problems 47 responses collected in January 2015, prior to convening Procedure: Each of 50 math problems rated on 2 criteria: 1. The relevance of the skill represented by the problem to performance in your entry-level course 2. The degree to which students bring this skill to your course 13

HIGHEST IMPORTANCE QUESTIONS 38. The graph on the right represents the closing price of a share of a certain stock for each day of a week. Which day had the greatest increase in the value of this stock over that of the previous day? A. Tuesday B. Wednesday C. Thursday D. Friday 14

HIGHEST IMPORTANCE, CONT’D. 5a. Len runs a mile in 8 minutes. At this rate how long will it take him to run a 26- mile marathon? A minutes B hoursC minutesD hours 39. The scatterplot on the right shows the ages of some children and the distance each child lives from school. Which statement BEST describes the relationship between age and distance from school? A. As age increases, the distance from school increases B. As age increases, the distance from school decreases. C. As age increases, the distance from school remains constant. D. There is no relationship between age and distance from school. 15

HIGHEST IMPORTANCE, CONT’D. 35. Which of the following is smallest? A B C D One hundred is multiplied by a number between 0 and 1. The answer has to be A. less than 0. B. between 0 and 50 but not 25. C. between 0 and 100 but not 50. D. between 0 and

HIGHEST IMPORTANCE RATINGS 17

LOWEST IMPORTANCE QUESTIONS 45. Calculate:log log 2 32 log log The points (1, 1), (2, 3), (4, 3), and (5, 1) are the vertices of a polygon. What type of polygon is formed by these points? A. Triangle B. Trapezoid C. ParallelogramD. Pentagon 24. A circle has its center at (6,7) and goes through point (1,4 ). A second circle is tangent to the first at point (1,4) and has the same area. What are the coordinates of the center of the second circle? 18

LOWEST IMPORTANCE, CONT’D. 43. Find the center, foci, vertices and co-vertices of this ellipse: (X - 2) 2 + (Y + 6) 2 = Use an inverse matrix to solve the linear system: -9X + 7Y = X -1Y =

LOWEST IMPORTANCE RATINGS 20

GRADE LEVEL AND IMPORTANCE 21

IMPORTANCE SCORES BY DISCIPLINE: HIGHEST 22 Grd 5 Grd 8 Grd 6

IMPORTANCE SCORES BY DISCIPLINE: LOWEST 23 HS A-Adv HS G 6 G

24 DISCIPLINARY EXAMPLES: Which math skills do students need in specific quantitative disciplines?

CATEGORIES OF MATH SKILLS NEEDED Arithmetic/Calculations/Number Sense Graphs Dimensional Analysis and Use of Symbols Linear and Simple Exponential Relationships Simple Algebra Problem Solving Statistics 25

BIOLOGY – SKILLS NEEDED Basic number sense – reasonableness of answers Graphing, especially starting from data and choosing axes and scale Dimensional Analysis Scientific notation, logarithms Simple algebra (such as Intro to Algebra or Elementary Algebra) Statistics

BIOLOGY SAMPLE PROBLEM 1.Choose a whale you want to draw, and find its maximum length in metric units. 2.Determine an optimum scale for your drawing to fit your paper, and show your calculations. 3.Calculate a conversion factor that allows you to translate the dimensions of the picture in the book into the sizes you should use in your drawing. Show your calculations.

CHEMISTRY – SKILLS NEEDED Order of operations, weighted averages, measuring volume Analysis of data and reasonableness of results Logarithms Algebra skills taught in Intro to Algebra Problem-solving skills Simple statistical concepts

CHEMISTRY SAMPLE PROBLEMS 1.Determine the volume of an object that has a mass of g and a density of 19.3 g/ given that D = m/V. 2. Write the answer to the following calculation in scientific notation, using the correct number of significant figures: ( – 333.9) x

GEOLOGY - SKILLS NEEDED Specializations have different needs, such as calculus for Geophysics; gradients for Meteorology General needs are: Graphing -- need to be able to start from data, not equations Rates of flow and averages

GEOLOGY SAMPLE PROBLEM A. From a local paper, find and record the following information for five consecutive days in an Excel spreadsheet: 1. High and low temperatures for the Dalles and Portland, converted into degrees Celsius. 2. Precipitation for both cities, converted into centimeters. B. Plot the information on two separate graphs, one for high/low temperatures, and the other for precipitation. Use a graphing program such as Excel, use titles for the graphs, and label the axes.

ECONOMICS – SKILLS NEEDED Expected value, weighted averages, index numbers Scatter plots and curve-fitting with technology Understand exponential growth Contextualized settings of the content Statistics Common sense interpretation The statistics taught in Math 105, Math in Society

ECONOMICS SAMPLE PROBLEM The following equations describe an economy (where quantities are in billions of dollars): C = Y D TA = 800 EX = 150 I = 100 TR = Y IM = 250 G = 480 Remember that Y D = Y – TA + TR and that in equilibrium Y = AE = C + I + G + EX – IM What is the equilibrium level of output (Y) for this economy? Show your work.

PHYSICS – SKILLS NEEDED Manipulate symbols without numbers in problems Use of units Problem-solving and critical thinking Applying simple math to solve problems Modeling – knowing which pieces of information to include or not Basic statistics

PHYSICS SAMPLE PROBLEM The final destination of a delivery truck is located 7.2 km in a direction 20 degrees South of West from its current position. If the truck travels 3.5 km due (directly) West, how far is it from its destination right now (straight line distance, “as the crow flies”)?

PSYCHOLOGY – SKILLS NEEDED Absolute value, percentage, basic arithmetic, rates of change Understand and use graphs, tables and charts Understand interactions of variables Independent vs. dependent variables Exponential vs. linear functions Middle school math Statistics Read and interpret; not necessarily calculate Understand correlation

PSYCHOLOGY SAMPLE PROBLEM To determine whether students would like more courses scheduled in the late afternoon and evening hours, 50 students selected at random from the 5,000 registered students were sent questionnaires. In this instance, the 5,000 students who are registered would be: a.A biased sample b.A population c.The dependent variable d.A representative sample

SOCIOLOGY – SKILLS NEEDED Creating and understanding graphs, slope, and intercepts Scientific notation, ratio and proportion Most of the algebra from Math 60 (Beginning Algebra) Mathematical modeling

SOCIOLOGY SAMPLE PROBLEM The 1936 Literary Digest presidential election poll predicted that Alf Landon would win the presidential election that year by a substantial majority. The poll was based on a sample of 2.4 million respondents drawn from three sources: 1) subscribers to the Literary Digest; 2) registered automobile owners; and 3) telephone users. Despite the poll’s prediction, Roosevelt beat Landon by a landslide. What might have gone wrong with the Literary Digest poll in this election?

NEXT STEPS Communicate with content area faculty Ensure students are aware of the best options for their career choices Become more aware of how math is applied in other content areas to develop appropriate pathways for students Incorporate content examples into everyday math work

CHALLENGES Sharing information from the February convening statewide Encouraging significant discussions that will lead to consensus within disciplines on the math skills needed for disciplines and career pathways Additional convening to dig deeper and include other disciplines?

Your thoughts?

43 MAHALO! Lisa Reynolds: For convening materials, resources, and further information: