Redefining Developmental Redefining Developmental Math for Non-Algebra Math for Non-Algebra Core Math  CoursesCore Math  Courses

Dr. Daryl StephensDr. Daryl Stephens

(stephen@etsu.edu)(stephen@etsu.edu)

Murray ButlerMurray Butler

(butlern@etsu.edu)(butlern@etsu.edu)

East Tennessee State East Tennessee State UniversityUniversity

DisclaimersDisclaimers

We don’t have all the answers. We don’t have all the answers.

We don’t even have all the questions!We don’t even have all the questions!

Your mileage may vary. (It may be that Your mileage may vary. (It may be that nothing in this presentation will apply nothing in this presentation will apply to your institution’s situation.)to your institution’s situation.)

ETSU’s SituationETSU’s Situation(Here’s where your mileage may vary.)(Here’s where your mileage may vary.) About 90% of our students do NOT About 90% of our students do NOT

take an algebra-based course (such as take an algebra-based course (such as college algebra, precalculus, calculus) college algebra, precalculus, calculus) for graduation. These students take for graduation. These students take MATH 1530, Probability and Statistics, MATH 1530, Probability and Statistics, as their core math class.as their core math class.

Very little intermediate algebra is Very little intermediate algebra is used in this course.used in this course.

ETSU’s SituationETSU’s Situation Mostly majors in math and the Mostly majors in math and the

sciences take something other than sciences take something other than prob & stat for graduation, and they prob & stat for graduation, and they are required to take one semester of are required to take one semester of calculus. (Digital media majors take calculus. (Digital media majors take both P&S and trig.) These students both P&S and trig.) These students benefit from intermediate algebra.benefit from intermediate algebra.

NSTCC and WSCC are affected by NSTCC and WSCC are affected by ETSU’s decisions.ETSU’s decisions.

Our Redesign ProposalOur Redesign Proposal

What did we think we would What did we think we would do?do?

Our Redesign Proposal Our Redesign Proposal (Briefly)(Briefly)

Re-vamp DSPM 0800 to make it a Re-vamp DSPM 0800 to make it a better preparation for statisticsbetter preparation for statistics

Delete DSPM 0850 requirement for Delete DSPM 0850 requirement for students not taking precalculus or students not taking precalculus or other algebra-based coursesother algebra-based courses

Same Topics, New Same Topics, New SequenceSequence

What concepts do the statisticians What concepts do the statisticians think the incoming student need?think the incoming student need?

Emphasize:Emphasize:

Order of operation, especially Order of operation, especially distributive property, even when distributive property, even when

using using a calculatora calculator Comparing (order) fractions, Comparing (order) fractions,

decimals, decimals, percents, and signed percents, and signed numbersnumbers

Interpret numerical answer—(what Interpret numerical answer—(what does it mean?)does it mean?)

continuedcontinued

Estimation: does the answer make Estimation: does the answer make sense?sense?

Percent, proportions, decimalsPercent, proportions, decimals Solving and graphing linear Solving and graphing linear

equationsequations The language of inequalitiesThe language of inequalities

Our Proposal – TechnologyOur Proposal – Technology Use My Math Lab, Hawkes Learning, or Use My Math Lab, Hawkes Learning, or

similar programs with both coursessimilar programs with both courses Alternate days between lecture Alternate days between lecture

classroom and computer lab as is classroom and computer lab as is done with statistics coursedone with statistics course

Do spreadsheet activities in Do spreadsheet activities in elementary algebra to prepare elementary algebra to prepare students for Minitabstudents for Minitab

Use graphing calculator in elementary Use graphing calculator in elementary algebra to prepare for stat and in algebra to prepare for stat and in intermediate algebra to prepare intermediate algebra to prepare students for precalculusstudents for precalculus

Envisioned AdvantagesEnvisioned Advantages

Cost savings: Cut back on sections of Cost savings: Cut back on sections of 0850 from ~12 each semester to ~3 0850 from ~12 each semester to ~3 or 4.or 4.

Prepare students for courses they Prepare students for courses they would actually takewould actually take

More individualized help with More individualized help with computer programs and computer programs and developmental math tutorsdevelopmental math tutors

DisadvantagesDisadvantages

Administration would be difficultAdministration would be difficult What about students who placed in What about students who placed in

0850? Move them on in to 1530 or 0850? Move them on in to 1530 or put them in 0800?put them in 0800?

What about students who change to What about students who change to science major after finishing science major after finishing 08000800→→1530?1530?

TBR DSP RedesignTBR DSP Redesign

Subcommittees working in all areas Subcommittees working in all areas including mathincluding math

Align with HS exit standardsAlign with HS exit standards This year’s 7This year’s 7thth graders (Class of 2013) graders (Class of 2013)

will have to take math all 4 years of high will have to take math all 4 years of high school!school!

New math curriculum standards based New math curriculum standards based on NCTM, ADP, ACT, NAEP, . . .on NCTM, ADP, ACT, NAEP, . . .

Math Redesign Math Redesign SubcommitteeSubcommittee Subcommittee includes university, Subcommittee includes university,

community college, and high school community college, and high school facultyfaculty

Currently surveying math and other Currently surveying math and other faculty across TBR to see what math is faculty across TBR to see what math is actually needed in intro and gen-ed actually needed in intro and gen-ed coursescourses

Some thought given to multiple exit Some thought given to multiple exit pointspoints

More questions than answers at this More questions than answers at this pointpoint

Committee’s ChargeCommittee’s Charge

Examine Examine whatwhat should be taught, should be taught, whenwhen, and , and whywhy..

Pilot programs help decide Pilot programs help decide who, howwho, how, , and and wherewhere..

Subcommittee Members

Chris Knight (Walters SCC) Co-chair John Kendall (SW TN) Co-chair Marva Lucas (MTSU) Helen Darcey (Cleveland SCC) Mary Monroe-Ellis (PSTCC) Sharon Lee (Wilson County Schools) Daryl Stephens (ETSU)

MATH Survey

The next few slides show a version of some questions that may be on the questionnaire to ask what math is needed in TBR core math classes with a prerequisite below the level of MATH 1xyz.

MATH 1010, 1110, 1130, 1410, 1420, 1530, 1630, 1710, 1720, 1730

Integrated ConceptsConnecting mathematics to other disciplines (real world

applications)

Connecting mathematics symbolically, numerically, graphically and verbally (Reading and interpreting graphs and tables, communicating mathematics, modeling)

Integrating technology (as a tool for problem solving and discovery)

Developing study skills (problem solving strategies, managing math anxiety, time management, feasibleness of solutions)

Analyze characteristics of functions (including domain, range, increasing, decreasing, and continuity)

Algebra and Number Sense

Perform operations on real numbers

Perform operations on complex numbers

Perform operations on polynomials (including factoring)

Analysis of linear functions and graphs (including inequalities)

Solve linear equations/inequalities

Analysis of quadratic functions and graphs (including inequalities)

Solve quadratic equations/inequalities

Analysis of rational functions and graphs (including inequalities)

(MATH continued)

Solve rational equations/inequalities

Analysis of radical functions and graphs (including inequalities)

Solve equations/inequalities with radical expressions

Analysis of exponential and logarithmic functions and graphs

Solve exponential and logarithmic equations

Unit conversions (mass, weight and volume in both standard and metric systems)

Solve systems of equations and inequalities

(MATH continued)

Introductory Probability and Statistics

Basic probability

Applying descriptive statistics ( of center and variation)

Organize and display data ( histograms, stems and leaf, pie charts, scatter plots)

Geometry

Geometric principles ( parallel line and transversals, sum of angles in plane figures, distance formula, midpoint formula, volume, and surface area)

Questionnaire for Non-Math

Division/Department

Please list the top prerequisite math skills needed in your program or course. Only include those courses that do

not already have a math prerequisite/corequisite. In other words, what math skills do your students need to have before they enter your class to have a reasonable

chance at success?

Program name or course rubric

  Math Skills List

1 . . . enter skills here . . . .

What to do now?What to do now?

Find money and/or share computer Find money and/or share computer spacespace

Move forward with the changes we Move forward with the changes we can makecan make

o Teach the important topics that prepare Teach the important topics that prepare students for statistics in our DSPM 0800 students for statistics in our DSPM 0800 then move students straight to Statisticsthen move students straight to Statistics

o Students needing Precalculus take DSPM Students needing Precalculus take DSPM 08500850

Proposed SequencesProposed Sequences

DSPM 0800 ContentDSPM 0800 Content(proposed)(proposed)

(Based on Martin-Gay combined 4th edition)

1. Review of Real Numbers1. Review of Real Numbers 1.2 Symbols and Sets of Numbers1.2 Symbols and Sets of Numbers 1.3 Fractions1.3 Fractions 1.4 Introduction to Variable 1.4 Introduction to Variable

Expressions and EquationsExpressions and Equations 1.5 Adding Real Numbers1.5 Adding Real Numbers 1.6 Subtracting Real Numbers1.6 Subtracting Real Numbers

1.7 Multiplying and Dividing Real 1.7 Multiplying and Dividing Real Numbers--Operations on Real Numbers--Operations on Real Numbers Numbers

1.8 Properties of Real Numbers1.8 Properties of Real Numbers

2.2. EquationsEquations 2.1 Simplifying Expressions2.1 Simplifying Expressions 2.2 The Addition and Multiplication 2.2 The Addition and Multiplication

Properties of Equality Properties of Equality 2.3 Solving Linear Equations2.3 Solving Linear Equations

2.4 An Introduction to Problem Solving2.4 An Introduction to Problem Solving 2.5 Formulas2.5 Formulas 2.6 Percent2.6 Percent 2.8 Linear Inequalities2.8 Linear Inequalities

3. Graphing3. Graphing 3.1 Reading Graphs & The 3.1 Reading Graphs & The

Rectangular Rectangular Coordinate SystemCoordinate System 3.2 Graphing Linear Equations3.2 Graphing Linear Equations

3.3 Intercepts3.3 Intercepts 3.4 Slope and Rate of Change3.4 Slope and Rate of Change 3.5 Slope-Intercept Form: 3.5 Slope-Intercept Form: y = mx + by = mx + b 3.6 The Point-Slope Form3.6 The Point-Slope Form 3.7 Functions3.7 Functions

4. Systems of Linear Equations4. Systems of Linear Equations 4.1 Solving Systems of Linear Equations 4.1 Solving Systems of Linear Equations

by Graphingby Graphing                         Integrated Review - Solving Integrated Review - Solving

Systems of EquationsSystems of Equations

5. Exponents and Polynomials5. Exponents and Polynomials 5.1 Exponents5.1 Exponents

9. Inequalities and Absolute Value9. Inequalities and Absolute Value 9.1 Compound Inequalities9.1 Compound Inequalities 9.4 Linear Inequalities in Two Variables 9.4 Linear Inequalities in Two Variables

and Systems of Linear Inequalitiesand Systems of Linear Inequalities

10. Radicals, Rational Exponents10. Radicals, Rational Exponents 10.1 Radicals and Radical Functions10.1 Radicals and Radical Functions

AppendicesAppendices D. An Introduction to Using a D. An Introduction to Using a

Graphing UtilityGraphing Utility G. Mean, Median, and ModeG. Mean, Median, and Mode

New DSPM 0850New DSPM 0850

5. Exponents and Polynomials5. Exponents and Polynomials 5.1 Exponents5.1 Exponents 5.2 Polynomial Functions and Adding and 5.2 Polynomial Functions and Adding and

Subtracting PolynomialsSubtracting Polynomials 5.3 Multiplying Polynomials5.3 Multiplying Polynomials 5.4 Special Products5.4 Special Products                         Integrated Review - Exponents Integrated Review - Exponents

and Operations on Polynomialsand Operations on Polynomials

5.5 Negative Exponents and Scientific 5.5 Negative Exponents and Scientific NotationNotation

5.6 Dividing Polynomials5.6 Dividing Polynomials 5.7 The Remainder Theorem5.7 The Remainder Theorem

6. Factoring Polynomials6. Factoring Polynomials 6.1 The Greatest Common Factor and 6.1 The Greatest Common Factor and

Factoring by GroupingFactoring by Grouping 6.2 Factoring Trinomials of the Form 6.2 Factoring Trinomials of the Form xx22

+ + bxbx + + cc

6.3 Factoring Trinomials of the Form 6.3 Factoring Trinomials of the Form axax22 + + bxbx + + cc and Perfect Square and Perfect Square TrinomialsTrinomials

6.4 Factoring Trinomials of the Form 6.4 Factoring Trinomials of the Form axax22 + + bxbx + + cc by Grouping by Grouping

6.5 Factoring Binomials6.5 Factoring Binomials                         Integrated Review-Choosing a Integrated Review-Choosing a

Factoring StrategyFactoring Strategy 6.6 Solving Quadratic Equations by 6.6 Solving Quadratic Equations by

FactoringFactoring 6.7 Quadratic Equations and Problem 6.7 Quadratic Equations and Problem

SolvingSolving

7. Rational Expressions7. Rational Expressions 7.1 Rational Functions and Simplifying 7.1 Rational Functions and Simplifying

Rational ExpressionsRational Expressions 7.2 Multiplying and Dividing Rational 7.2 Multiplying and Dividing Rational

ExpressionsExpressions 7.3 Adding and Subtracting Rational 7.3 Adding and Subtracting Rational

Expressions with Common Denominators Expressions with Common Denominators and Least Common Denominatorand Least Common Denominator

7.4 Adding and Subtracting Rational 7.4 Adding and Subtracting Rational Expressions with Unlike  DenominatorsExpressions with Unlike  Denominators

7.5 Solving Equations Containing 7.5 Solving Equations Containing Rational ExpressionsRational Expressions

                        Integrated Review-Summary Integrated Review-Summary on Rational Expressionson Rational Expressions

7.6 Proportion and Problem Solving 7.6 Proportion and Problem Solving with Rational Equationswith Rational Equations

7.7 Simplifying Complex Fractions7.7 Simplifying Complex Fractions

     10. Radicals, Rational Exponents, 10. Radicals, Rational Exponents,

and Complex Numbersand Complex Numbers 10.2 Rational Exponents10.2 Rational Exponents

10.3 Simplifying Radical Expressions10.3 Simplifying Radical Expressions 10.4 Adding and Subtracting and 10.4 Adding and Subtracting and

Multiplying Radical ExpressionsMultiplying Radical Expressions 10.5 Rationalizing Denominators and 10.5 Rationalizing Denominators and

Numerators of Radical ExpressionsNumerators of Radical Expressions                         Integrated Review - Radicals Integrated Review - Radicals

and Rational Exponentsand Rational Exponents 10.6 Radical Equations and Problem 10.6 Radical Equations and Problem

SolvingSolving 10.7 Complex Numbers10.7 Complex Numbers

11. Quadratic Equations and 11. Quadratic Equations and FunctionsFunctions

11.1 Solving Quadratic Equations by 11.1 Solving Quadratic Equations by Completing the SquareCompleting the Square

11.2 Solving Quadratic Equations by 11.2 Solving Quadratic Equations by the Quadratic Formulathe Quadratic Formula

11.3 Solving Equations by Using 11.3 Solving Equations by Using Quadratic MethodsQuadratic Methods

                Integrated Review-Summary on Integrated Review-Summary on Solving Quadratic EquationsSolving Quadratic Equations

11.5 Quadratic Functions and Their 11.5 Quadratic Functions and Their GraphsGraphs

11.6 Further Graphing of Quadratic 11.6 Further Graphing of Quadratic FunctionsFunctions

   4. Systems of Linear Equations4. Systems of Linear Equations 4.2 Solving Systems of Linear 4.2 Solving Systems of Linear

Equations by SubstitutionEquations by Substitution 4.3 Solving Systems of Linear 4.3 Solving Systems of Linear

Equations by AdditionEquations by Addition

                Integrated Review - Solving Integrated Review - Solving Systems of EquationsSystems of Equations

4.5 Systems of Linear Equations and 4.5 Systems of Linear Equations and Problem SolvingProblem Solving

*12. Exponential and Logarithmic *12. Exponential and Logarithmic FunctionsFunctions

12.1 The Algebra of Functions: 12.1 The Algebra of Functions: Composite FunctionsComposite Functions

12.2 Inverse Functions12.2 Inverse Functions

*12. Exponential and Logarithmic *12. Exponential and Logarithmic FunctionsFunctions

12.1 The Algebra of Functions: 12.1 The Algebra of Functions: Composite FunctionsComposite Functions

12.2 Inverse Functions12.2 Inverse Functions 12.3 Exponential Functions12.3 Exponential Functions 12.4 Logarithmic Functions12.4 Logarithmic Functions 12.7 Exponential and Logarithmic 12.7 Exponential and Logarithmic

Equations and ApplicationsEquations and Applications

*Optional*Optional

Questions?Questions? Answers?Answers?

Comments?Comments?Suggestions?Suggestions?Complaints?Complaints?

Thanks for coming!Thanks for coming!

This presentation will be on Daryl’s This presentation will be on Daryl’s faculty web page:faculty web page:http://faculty.etsu.edu/stephen/handouts.htm

Look for links from that page.Look for links from that page.