Redefining Developmental Math for Non-Algebra Core Math Courses Dr. Daryl Stephens...
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Transcript of Redefining Developmental Math for Non-Algebra Core Math Courses Dr. Daryl Stephens...
Redefining Developmental Redefining Developmental Math for Non-Algebra Math for Non-Algebra Core Math CoursesCore Math Courses
Dr. Daryl StephensDr. Daryl Stephens
([email protected])([email protected])
Murray ButlerMurray Butler
([email protected])([email protected])
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.