maa joint mtg jan2013 san diego 1.11.13

7/30/2019 MAA Joint Mtg Jan2013 San Diego 1.11.13

1/39

Transition to CollegeMathematics and Statistics

for Non-STEM Students

Joint Mathematics Meetings

January 9-12, 2013San Diego, CA

Christian R. Hirsch


2/39

Session Overview

2

Why TCMS?

Design of TCMS

Units and Key Topics

Comments and Questions


3/39

3

Transition Issues

Unacceptably high enrollments in non-credit bearingcourses


4/39


5/39

Transition Issues

5


Three years of college preparatory mathematics isinsufficient for college readiness


6/39

6

In the 2009-2010 administration of the Ohio EarlyMathematics Placement Testing, based on theexpressed intended majors of test-takers, 63% ofthe test-takers would place in a remedial (non-credit

bearing) course in college if they took no furthermathematics in high school.

E. Laughbaum, personal communication, January 5, 2013


7/39

Transition Issues

7


Three years of college preparatory mathematics is

insufficient for college readiness Preparation for college mathematics is not

necessarily preparation for calculus and vice versa


8/39

8

Fall 2010 Four-Year College Mathematics

and Statistics Enrollments1 Approximately 25% of students took mainstream or non-mainstream

Calculus I or II.

Approximately 10% of students took a noncalculus-based course instatistics.

Approximately 7% of students took a Liberal Arts Mathematics course.

Approximately 6% of students took a Finite or Business Mathematicscourse.

Approximately 4% of students took an Elementary Education Mathematicscourse.

These data suggest that for a large number of students, success in

college is dependent on mathematics coursework that is independentof calculus instruction.

12010 Preliminary Results from the Statistical Abstract of UndergraduatePrograms in the Mathematical Sciences in the United States.

http://www.ams.org/profession/data/cbms-survey/cbms2010-work
http://www.ams.org/profession/data/cbms-survey/cbms2010-workhttp://www.ams.org/profession/data/cbms-survey/cbms2010-workhttp://www.ams.org/profession/data/cbms-survey/cbms2010-workhttp://www.ams.org/profession/data/cbms-survey/cbms2010-workhttp://www.ams.org/profession/data/cbms-survey/cbms2010-workhttp://www.ams.org/profession/data/cbms-survey/cbms2010-work


9/39

Transition Issues

9


Three years of college preparatory mathematics is

insufficient for college readiness Preparation for college mathematics is not

necessarily preparation for calculus

Weak alignment between university mathematics

placement tests (and sometimes courses) and bothhigh school mathematics priorities and professionalrecommendations for undergraduate mathematics.


10/39

MAA Curriculum Foundations Project

Summary Recommendations

10

Emphasize conceptual understanding

Emphasize problem-solving skills

Emphasize mathematical modeling

Emphasize communication skills

Emphasize balance between mathematical

perspectives (e.g., continuous and discrete,deterministic and stochastic)

Ganter & Barker (2004)


11/39

11

Transition to College Mathematics and Statisticsis an alternative fourth-year mathematical

sciences course designed to support college-

readiness of non-STEM students. It is the product

of three years of research, development, and

evaluation funded by the National Science

Foundation.


12/39

12

Algebra and Functions

Bernie Madison University of Arkansas

Development Process and Consultants

Discrete Mathematics

Steve Maurer Swarthmore College

GeometryDoris Schattschneider Moravian College

Statistics and Probability

Christine Franklin University of Georgia


13/39

TCMS Design Features

13

Development of mathematics as an active science of patterns Course organized around interwoven strands of algebra and

functions, geometry and trigonometry, statistics and probability, and

discrete mathematics

Mathematical strands developed in coherent, focused units that

exploit connections to the other strands

New mathematical ideas introduced in the context of problem

situations

Focus on applications and mathematical modeling

Emphasis on small-group collaborative learning and sense-making

Full and strategic use of technology tools


14/39

14


15/39

VIDEO GAME SYSTEM PRODUCTION

PROFITThe manager of TK Electronicsmust plan for production of two

video game systems, a standard

model (SM) and a deluxe model

(DM).

Given the following production

limits for assembly time, testing

time, and packaging time, how

should the manager planproduction to maximize profit for

his company?

15


16/39

Production Conditions

16

Assembly of each SM game system takes 0.6 hours of

technician time and assembly of each DM game system takes

0.3 hours of technician time. The plant limits technician time to at

most 240 hours per day.

Testing for each SM system takes 0.2 hours and testing of eachDM system takes 0.4 hours. The plant can apply at most 160

hours of technician time each day for testing.

Packaging time is the same for each model. The packaging

department of the plant can handle at most 500 game systemsper day.

The company makes a profit of $50 on each SM model and $75

on each DM model.


17/39

17


18/39

18


19/39

19


20/39

20


21/39

21


22/39

22


23/39


24/39

Transition to College Mathematics and

Statistics

Units and Key Topics

24

Unit 1: Interpreting Categorical Data

Develops student understanding of two-way frequencytables, conditional probability and independence, andusing data from a randomized experiment to compare

two treatments .

Topics include two-way tables, graphical representations,comparison of proportions including absolute riskreduction and relative risk, characteristics and

terminology of well-designed experiments, expectedfrequency, chi-square test of homogeneity, statisticalsignificance.


25/39

25

Unit 2: Functions Modeling Change

Extends student understanding of linear, exponential,quadratic, power, trigonometric, and logarithmicfunctions to model quantitative relationships and data

patterns whose graphs are transformations of basicpatterns.

Topics include linear, exponential, quadratic, power,circular, and base-10 logarithmic functions;mathematical modeling; translation, reflection,stretching, and compressing of graphs withconnections to symbolic forms of correspondingfunction rules.


Statistics


26/39

26

Unit 3: Counting Methods

Extends student ability to count systematically and solveenumeration problems using permutations andcombinations.

Topics include systematic listing and counting, countingtrees, the Multiplication Principle of Counting, AdditionPrinciple of Counting, combinations, permutations,selections with repetition; the binomial theorem, Pascals

triangle, combinatorial reasoning; and the generalmultiplication rule for probability.


Statistics


27/39

27

Unit 4: Quantitative and Algebraic Reasoning

Extends student facility with the use of functions,expressions, and equations in representing andreasoning about quantitative relationships, especially

those involving financial mathematical models andbivariate data.

Topics include investments and compound interest,continuous compounding and natural logarithms, andamortization of loans; linearization of bivariate datausing log and log-log transformations; and solution ofequations involving logarithms, absolute value, andradical expressions.


Statistics


28/39

28

Unit 5: Binomial Distributions and Statistical Inference

Develops student understanding of the rules of probability; binomialdistributions; expected value; testing a model; simulation; makinginferences about the population based on a random sample; marginof error; and comparison of sample surveys, experiments, and

observational studies and how randomization relates to each.

Topics include review of basic rules and vocabulary of probability(addition and multiplication rules, independent events, mutuallyexclusive events); binomial probability formula; expected value;statistical significance and P-value; design of sample surveysincluding random sampling and stratified random sampling; responsebias; sample selection bias; sampling distribution; variability insampling and sampling error; margin of error; and confidenceinterval.


Statistics


29/39

29

Unit 6: Informatics

Develops student understanding of the mathematicalconcepts and methods related to informationprocessing, particularly on the Internet, focusing on the

key issues of access, security, accuracy, and efficiency.

Topics include elementary set theory and logic; modulararithmetic and number theory; secret codes, symmetric-key and public-key cryptosystems; error-detectingcodes (including ZIP, UPC, and ISBN) and error-correcting codes (including Hamming distance); andtrees and Huffman coding.


Statistics


30/39

30

Unit 7: Spatial Visualization and Representations

Extends student ability to visualize and represent three-dimensional shapes using contour diagrams, cross sections, andrelief maps; to use coordinate methods for representing andanalyzing three-dimensional shapes and their properties; and to

use geometric and algebraic reasoning to solve systems of linearequations and inequalities in three variables and linearprogramming problems.

Topics include using contours to represent three-dimensionalsurfaces and developing contour maps from data; sketchingsurfaces from sets of cross sections; three-dimensional rectangularcoordinate system; sketching planes using traces, intercepts, andcross sections derived from algebraic representations; systems oflinear equations and inequalities in three variables; and linearprogramming.


Statistics


31/39

31

Unit 8: Mathematics of Democratic Decision-Making

Develops student understanding of the mathematicalconcepts and methods useful in making decisions in ademocratic society, as related to voting, fair division, andgame theory.

Topics include preferential voting and associated vote-analysis methods such as majority, plurality, runoff, points-for-preferences (Borda method), pairwise-comparison(Condorcet method), and Arrows theorem; weighted voting,

including weight and power of a vote and the Banzhaf powerindex; fair division techniques, including apportionmentmethods; and game theory, including zero-sum and non-zero-sum games, Nashs theorem, and the minimax theorem.


Statistics


32/39

32

Voices of TCMS Teachers

What do you see as the major strengths of TCMS?

It reaches out to a select population of students that we previouslyhad nothing to offer them.

TCMS is the perfect class for collaborative learning. Studentslearn to actually read in a math class, they learn how to makemistakes and learn from them as opposed to being discouraged bythem, and they also get a deeper understanding of themathematical material since the topics are all in a real-world

context.


33/39

33

This course really made the teacher and students thinkabout the mathematics being taught and learned. It gave alot of students who were unsuccessful in Algebra 2 anopportunity to be successful. They enjoyed most topics andthe contexts were very engaging. Many of my students leftat the end with a view of mathematics as being useful.

One of the strengths is the connection that TCMS makes tothe professional careers that exist today. Students can seethe relevance in learning the mathematics, even if its not

[always] the field of study they are interested in.


34/39

34

Comments and Questions


35/39

35

Preliminary Findings

1. Based on the TCMS Post Belief Survey, students across all 6field-test schools generally found

the Statistics and Coding /Cryptography units to be mostinteresting, and noted the mathematics reasonable to

understand, but particularly noted that the contexts werevery very interesting and something they could relate to.

students from traditional schools couched many of theircomments (e.g., those related to the real-world problems) asa contrast to the non-context experiences they encountered

in their previous Algebra and Geometry courses.


36/39

36

2. Based on the ITED Pre/Post highest level Quantitative ThinkingTest (a 40-item test focusing on thinking and reasoning skills),

students at

all schools showed pre-post gains at least slightly greater thanexpected (national) norms (an identical mean in spring to fallwould be normal growth).

one CPMP background school made significant gains at thep=.05 level; one traditional school at the p.05 level, and one atthe p=.10 level.

Across all schools, gains were particularly notable for students inthe 3rd and 4th quartiles.


37/39

37

3. Based on the Conceptions of Mathematics Pre/Post Inventory,students

Most changes within seven grouped (item) categoriesinvolved changes toward a conception of Mathematics asConcepts more than Procedures and Sense-Making morethan Memorizing.

4. We are in the process of contacting and collecting 1st semestercollege data from students.


38/39

38

Voices of TCMS StudentsWould you recommend this course to students (juniors)considering a math course to take for next year? What topics didyou find most interesting? Least interesting or most difficult?

Yes, because it seems like we learn things that are much

more applicable to daily life than other math classes. Myfavorite was creating codes.

This course takes skills and ideas learned from previouscourses, reviews them, and expands upon the conceptsthat may have been misunderstood previously. Mostinteresting: Different voting methods gave differentoutcomes. Most Difficult: Some of the graphing we wererequired to do, involving transformations especially.


39/39

39

It was a good class to take because the concepts are fairlyeasy, but they are different from every other math class.

I think this class will prepare you for college with the layout ofthe class you get to learn many different types of math.Interestingstatistics were most interesting it related a lot to

real life. Most difficult were some of the graphs and knowinghow to read them.

maa joint mtg jan2013 san diego 1.11.13

Documents