Which Math? Dan Yasaki Department of Mathematics and Statistics - - PowerPoint PPT Presentation

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Which Math? Dan Yasaki Department of Mathematics and Statistics The University of North Carolina at Greensboro December 3, 2018 Coffee and Conversation Event Dan Yasaki Which Math? 1 / 45 Things to consider when selecting a math course

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Which Math?

Dan Yasaki

Department of Mathematics and Statistics The University of North Carolina at Greensboro

December 3, 2018 Coffee and Conversation Event

Dan Yasaki Which Math? 1 / 45

SLIDE 2

Things to consider when selecting a math course

Mathematical maturity Mathematical training

Previous math courses Math Placement Test (MPT) score AP Exam score

Time since last math course Goals Interests and strengths Program requirements Skills (job, life)

Dan Yasaki Which Math? 2 / 45

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Things to consider when selecting a math course

Mathematical maturity Mathematical training

Previous math courses Math Placement Test (MPT) score AP Exam score

Time since last math course Goals Interests and strengths Program requirements Skills (job, life)

Dan Yasaki Which Math? 2 / 45

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GMT courses

STA 108: Elementary Intro to Probability and Statistics CSC 110: Computational Problem Solving MAT 112: Contemporary Topics in Mathematics MAT 115: College Algebra MAT 120: Calculus with Business Applications MAT 150: Precalculus I MAT 151: Precalculus II MAT 190: Precalculus MAT 191: Calculus I MAT 253: Discrete Mathematical Structures MAT 292: Calculus II Math Placement Test (MPT) below 60%; AP Calculus score below 2; AP Statistics score below 3.

Dan Yasaki Which Math? 3 / 45

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GMT courses without prerequisites

STA 108: Elementary Intro to Probability and Statistics CSC 110: Computational Problem Solving MAT 112: Contemporary Topics in Mathematics MAT 115: College Algebra MAT 120: Calculus with Business Applications MAT 150: Precalculus I MAT 151: Precalculus II MAT 190: Precalculus MAT 191: Calculus I MAT 253: Discrete Mathematical Structures MAT 292: Calculus II Math Placement Test (MPT) below 60%; AP Calculus score below 2; AP Statistics score below 3.

Dan Yasaki Which Math? 3 / 45

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GMT courses MPT/AP MAT 150 MAT 151 MAT 115 MAT 120 MAT 112 STA 108 MAT 253 MAT 190 MAT 191

Dan Yasaki Which Math? 4 / 45

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GMT courses without prerequisites MPT/AP MAT 150 MAT 151 MAT 115 MAT 120 MAT 112 STA 108 MAT 253 MAT 190 MAT 191

Dan Yasaki Which Math? 5 / 45

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GMT courses without prerequisites: STA 108

STA 108: Elementary Introduction to Probability and Statistics A statistical literacy course. Best for students who plan to take only one math/stat course; and will never do any statistical analyses but may need to be “knowledgeable consumers” of statistics. STA 108 exposes students to the basic statistical rudiments necessary to be an informed member of society in today’s data-driven world.

Dan Yasaki Which Math? 6 / 45

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GMT courses without prerequisites: STA 108

STA 108: Elementary Introduction to Probability and Statistics A statistical literacy course. Best for students who plan to take only one math/stat course; and will never do any statistical analyses but may need to be “knowledgeable consumers” of statistics. STA 108 exposes students to the basic statistical rudiments necessary to be an informed member of society in today’s data-driven world.

Dan Yasaki Which Math? 6 / 45

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STA 108: Elementary Intro to Probability and Statistics

Additional notes Likely a terminal statistics course. Not “easy” GMT course, but starts from scratch. Does not assume fluency high school algebra. Includes some “different” mathematics (outside the scope

f what is typically taught in high school).

Dan Yasaki Which Math? 7 / 45

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GMT courses without prerequisites: MAT 112

MAT 112: Contemporary Topics in Mathematics A mathematical literacy course. Best for students who plan to take only one math/stat course; and have interest or will work in areas that value structure and exactness. MAT 112 exposes students to precise formulations and logical reasoning, demystifying certain mathematical constructions that are relevant for the digital age.

Dan Yasaki Which Math? 8 / 45

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GMT courses without prerequisites: MAT 112

MAT 112: Contemporary Topics in Mathematics A mathematical literacy course. Best for students who plan to take only one math/stat course; and have interest or will work in areas that value structure and exactness. MAT 112 exposes students to precise formulations and logical reasoning, demystifying certain mathematical constructions that are relevant for the digital age.

Dan Yasaki Which Math? 8 / 45

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MAT 112: Contemporary Topics in Mathematics

Additional notes Terminal math course. Not “easy” GMT course, but starts from scratch. Does not assume fluency in high school algebra. Includes some “different” mathematics (outside the scope

f what is typically taught in high school).

Dan Yasaki Which Math? 9 / 45

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STA 108 versus MAT 112

STA 108 is good for future consumers of statistics. MAT 112 develops skills in logic and dealing with structured languages.

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GMT courses without prerequisites: MAT 115

MAT 115: College Algebra An introductory algebra course. Best for students who will work in areas that need a mastery of basic algebraic skills; or intend to take MAT 120: Calculus with Business Applications. MAT 115 introduces standard algebra techniques, training students to be able to perform basic algebraic manipulations that may arise in other contexts.

Dan Yasaki Which Math? 11 / 45

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GMT courses without prerequisites: MAT 115

MAT 115: College Algebra An introductory algebra course. Best for students who will work in areas that need a mastery of basic algebraic skills; or intend to take MAT 120: Calculus with Business Applications. MAT 115 introduces standard algebra techniques, training students to be able to perform basic algebraic manipulations that may arise in other contexts.

Dan Yasaki Which Math? 11 / 45

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MAT 115: College Algebra

Additional notes Assumes some fluency in high school algebra. Primarily for students whose program requires it. Not recommended as “generic” GMT course. C is required to progress to MAT 120: Calculus with Business Applications.

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GMT courses without prerequisites: MAT 150

MAT 150: Precalculus I An introductory precalculus course. Best for students who will work in areas that need a mastery of basic algebraic skills; or intend to take MAT 191: Calculus I, after also completing MAT 151: MAT 150 covers similar topics to MAT 115. It is the first semester of a two semester sequence of precalculus.

Dan Yasaki Which Math? 13 / 45

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GMT courses without prerequisites: MAT 150

MAT 150: Precalculus I An introductory precalculus course. Best for students who will work in areas that need a mastery of basic algebraic skills; or intend to take MAT 191: Calculus I, after also completing MAT 151: MAT 150 covers similar topics to MAT 115. It is the first semester of a two semester sequence of precalculus.

Dan Yasaki Which Math? 13 / 45

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MAT 150: Precalculus I

Additional notes Assumes some fluency in high school algebra. Primarily for students whose program requires it. Goes into more depth than MAT 115. Not recommended as “generic” GMT course. C is required to progress to MAT 151: Precalculus II.

Dan Yasaki Which Math? 14 / 45

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MAT 115 versus MAT 150

MAT 115 is more computation than theory. MAT 150 goes into more depth, with an additional focus on writing and explaining concepts. MAT 115 leads to MAT 120: Calculus with Business Applications. The MAT 150–151 sequence leads to MAT 191: Calculus I.

Dan Yasaki Which Math? 15 / 45

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GMT courses without prerequisites: MAT 253

MAT 253: Discrete Mathematical Structures An introductory discrete math course. Best for students who are more mathematically mature; like mathematics; and want to see “different” mathematics (outside the scope of what is typically offered in high school). MAT 253 is an introduction to discrete structures and rigor. Topics may overlap some with MAT 112.

Dan Yasaki Which Math? 16 / 45

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GMT courses without prerequisites: MAT 253

MAT 253: Discrete Mathematical Structures An introductory discrete math course. Best for students who are more mathematically mature; like mathematics; and want to see “different” mathematics (outside the scope of what is typically offered in high school). MAT 253 is an introduction to discrete structures and rigor. Topics may overlap some with MAT 112.

Dan Yasaki Which Math? 16 / 45

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MAT 253: Discrete Mathematical Structures

Additional notes Assumes higher level of mathematical fluency. Introduction to mathematical rigor. Includes an introduction to programming in Python.

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MAT 112 versus MAT 253

MAT 112 assumes less comfort with math. MAT 253 can be part of a mathematics minor. MAT 253 develops the theory alongside the computations, allowing for deeper understanding of discrete structures.

Dan Yasaki Which Math? 18 / 45

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GMT courses

STA 108: Elementary Intro to Probability and Statistics CSC 110: Computational Problem Solving MAT 112: Contemporary Topics in Mathematics MAT 115: College Algebra MAT 120: Calculus with Business Applications MAT 150: Precalculus I MAT 151: Precalculus II MAT 190: Precalculus MAT 191: Calculus I MAT 253: Discrete Mathematical Structures MAT 292: Calculus II 1 or 0 semester preparation before goal of MAT 120: Calculus with Business Applications.

Dan Yasaki Which Math? 19 / 45

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GMT courses for the Business track

STA 108: Elementary Intro to Probability and Statistics CSC 110: Computational Problem Solving MAT 112: Contemporary Topics in Mathematics MAT 115: College Algebra MAT 120: Calculus with Business Applications MAT 150: Precalculus I MAT 151: Precalculus II MAT 190: Precalculus MAT 191: Calculus I MAT 253: Discrete Mathematical Structures MAT 292: Calculus II 1 or 0 semester preparation before goal of MAT 120: Calculus with Business Applications.

Dan Yasaki Which Math? 19 / 45

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GMT courses MPT/AP MAT 150 MAT 151 MAT 115 MAT 120 MAT 112 STA 108 MAT 253 MAT 190 MAT 191

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GMT courses for the Business track MPT/AP MAT 150 MAT 151 MAT 115 MAT 120 MAT 112 STA 108 MAT 253 MAT 190 MAT 191

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GMT courses for the Business track: MAT 120

MAT 120: Calculus with Business Applications An applied differential calculus course. Best for students who will work in areas that use standard calculus techniques in applications; or want a terminal calculus course. MAT 120 exposes students to calculus through applications, with an emphasis on applications in business and social sciences.

Dan Yasaki Which Math? 22 / 45

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GMT courses for the Business track: MAT 120

MAT 120: Calculus with Business Applications An applied differential calculus course. Best for students who will work in areas that use standard calculus techniques in applications; or want a terminal calculus course. MAT 120 exposes students to calculus through applications, with an emphasis on applications in business and social sciences.

Dan Yasaki Which Math? 22 / 45

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MAT 120: Calculus with Business Applications

Additional notes Terminal math course. Not adequate preparation for MAT 292: Calculus II.

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1 semester preparation before MAT 120

MPT < 60% and AP < 2 MAT 150 MAT 115 MAT 120

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0 semester preparation before MAT 120 MPT ≥ 60% or AP = 2 MAT 120

MPT 60% or higher allows registration for MAT 120. AP Calculus score 2 allows registration for MAT 120. AP Calculus score 3 or higher gives credit for MAT 191.

Dan Yasaki Which Math? 25 / 45

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GMT courses

STA 108: Elementary Intro to Probability and Statistics CSC 110: Computational Problem Solving MAT 112: Contemporary Topics in Mathematics MAT 115: College Algebra MAT 120: Calculus with Business Applications MAT 150: Precalculus I MAT 151: Precalculus II MAT 190: Precalculus MAT 191: Calculus I MAT 253: Discrete Mathematical Structures MAT 292: Calculus II 2, 1, or 0 semesters preparation before MAT 191: Calculus I.

Dan Yasaki Which Math? 26 / 45

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GMT courses for the Calculus track

STA 108: Elementary Intro to Probability and Statistics CSC 110: Computational Problem Solving MAT 112: Contemporary Topics in Mathematics MAT 115: College Algebra MAT 120: Calculus with Business Applications MAT 150: Precalculus I MAT 151: Precalculus II MAT 190: Precalculus MAT 191: Calculus I MAT 253: Discrete Mathematical Structures MAT 292: Calculus II 2, 1, or 0 semesters preparation before MAT 191: Calculus I.

Dan Yasaki Which Math? 26 / 45

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GMT courses MPT/AP MAT 150 MAT 151 MAT 115 MAT 120 MAT 112 STA 108 MAT 253 MAT 190 MAT 191

Dan Yasaki Which Math? 27 / 45

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GMT courses for the Calculus track MPT/AP MAT 150 MAT 151 MAT 115 MAT 120 MAT 112 STA 108 MAT 253 MAT 190 MAT 191

Dan Yasaki Which Math? 28 / 45

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GMT courses for the Calculus track: MAT 151

MAT 151: Precalculus II A second precalculus course. Best for students who have credit for MAT 115 or MAT 150 and

will work in areas that need a mastery of certain transcendental functions; or intend to take MAT 191: Calculus.

MAT 151 is the second half of a two semester sequence of precalculus, exposing students to the properties, graphs, and applications of certain transcendental functions.

Dan Yasaki Which Math? 29 / 45

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GMT courses for the Calculus track: MAT 151

MAT 151: Precalculus II A second precalculus course. Best for students who have credit for MAT 115 or MAT 150 and

will work in areas that need a mastery of certain transcendental functions; or intend to take MAT 191: Calculus.

MAT 151 is the second half of a two semester sequence of precalculus, exposing students to the properties, graphs, and applications of certain transcendental functions.

Dan Yasaki Which Math? 29 / 45

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GMT courses for the Calculus track: MAT 190

MAT 190: Precalculus A precalculus course. Best for students who sufficiently strong background in mathematics; and

will work in areas that need a mastery of certain transcendental functions; or intend to take MAT 191: Calculus I.

MAT 190 is one semester course in precalculus. Coursework previews calculus concepts, focuses heavily on organizing and writing solutions.

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GMT courses for the Calculus track: MAT 190

MAT 190: Precalculus A precalculus course. Best for students who sufficiently strong background in mathematics; and

will work in areas that need a mastery of certain transcendental functions; or intend to take MAT 191: Calculus I.

MAT 190 is one semester course in precalculus. Coursework previews calculus concepts, focuses heavily on organizing and writing solutions.

Dan Yasaki Which Math? 30 / 45

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MAT 190: Precalculus

Additional notes Offered only in lecture/lab format (3:3:1). Lab activities include additional examples and application. Fast-paced and intense preparation for calculus. C is required to progress to MAT 191: Calculus I.

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GMT courses for the Calculus track: MAT 191

MAT 191: Calculus I A differential calculus course. Best for students who will work in areas that use differential calculus techniques and theory; or intend to take MAT 292: Calculus II. MAT 191 is the first of a four semester calculus sequence.

Dan Yasaki Which Math? 32 / 45

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GMT courses for the Calculus track: MAT 191

MAT 191: Calculus I A differential calculus course. Best for students who will work in areas that use differential calculus techniques and theory; or intend to take MAT 292: Calculus II. MAT 191 is the first of a four semester calculus sequence.

Dan Yasaki Which Math? 32 / 45

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MAT 191: Calculus I

Additional notes 3 or higher on AP Calculus Exam grants credit. Primarily for STEM (science, technology, engineering, and math) or Economics. C is required to progress to MAT 292: Calculus II.

Dan Yasaki Which Math? 33 / 45

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MAT 120 versus MAT 191

MAT 120 is a terminal calculus course. MAT 191 allows students to continue in the calculus sequence. MAT 120 surveys topics with an eye toward applications. MAT 191 develops the theory alongside the computations, allowing for deeper understanding of calculus.

Dan Yasaki Which Math? 34 / 45

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2 semester preparation before MAT 191

MPT < 60% and AP < 2 MAT 150 MAT 115 MAT 151 MAT 191

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1 semester preparation before MAT 191 MPT ≥ 60% or AP = 2 MAT 190 MAT 191

MPT 80% or higher allows registration for MAT 191. AP Calculus score 2 allows registration for MAT 191. AP Calculus score 3 or higher gives credit for MAT 191.

Dan Yasaki Which Math? 36 / 45

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0 semester preparation before MAT 191 MPT ≥ 80% or AP = 2 MAT 191

MPT 80% or higher allows registration for MAT 191. AP Calculus score 2 allows registration for MAT 191. AP Calculus score 3 or higher gives credit for MAT 191.

Dan Yasaki Which Math? 37 / 45

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Math Pathways

The UNC System has engaged with the Charles A. Dana Center to mobilize mathematics faculty in North Carolina to improve student success.

dcmathpathways.org/where-we-work/north-carolina

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Dana Center Mathematics Pathways Model: Principles

All students, regardless of college readiness, enter directly into mathematics pathways aligned to their programs of study. Students complete their first college-level mathematics requirement in their first year of college. Strategies to support students as learners are integrated into courses and are aligned across the institution. Instruction incorporates evidence-based curriculum and pedagogy.

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Moving the Metrics: Calculus Corequisite Pilot

Over 40% of those who attempt MAT 191 never achieve a grade of C or better. Among those who do, very few succeed in their first year of study.

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Moving the Metrics: MAT 181

MAT 181: Foundations of Calculus I A corequisite support course for MAT 191. Best for students who will concurrently enroll in MAT 191; and need additional support to succeed in MAT 191. MAT 181 provides supplemental just-in-time support for at-risk students in MAT 191.

MAT 181 MAT 191

Dan Yasaki Which Math? 41 / 45

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Moving the Metrics: MAT 181

MAT 181: Foundations of Calculus I A corequisite support course for MAT 191. Best for students who will concurrently enroll in MAT 191; and need additional support to succeed in MAT 191. MAT 181 provides supplemental just-in-time support for at-risk students in MAT 191.

MAT 181 MAT 191

Dan Yasaki Which Math? 41 / 45

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MAT 181: Foundations of Calculus I

Additional notes Spring 2019: TR 3:30–4:45 pm or MWF 10:00–10:50 am (Moving the Metrics). Requires concurrent registration in MAT 191. Allows students missing formal prerequisites to register for MAT 191. Open to students that meet the prerequisites for MAT 191 but self-identify as at-risk. Additional sections in Fall 2019 and Spring 2020 (College support).

Dan Yasaki Which Math? 42 / 45

SLIDE 57

Math Pathways

Assess placement practices. Communicate with departments about aligning math requirements with program goals.

Design new courses. Revise existing courses.

Explore additional support structures.

Corequisite support courses. Recitation sections. Alternative modes of course delivery.

Dan Yasaki Which Math? 43 / 45

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Math Pathways

Assess placement practices. Communicate with departments about aligning math requirements with program goals.

Design new courses. Revise existing courses.

Explore additional support structures.

Corequisite support courses. Recitation sections. Alternative modes of course delivery.

Dan Yasaki Which Math? 43 / 45

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Math Pathways

Assess placement practices. Communicate with departments about aligning math requirements with program goals.

Design new courses. Revise existing courses.

Explore additional support structures.

Corequisite support courses. Recitation sections. Alternative modes of course delivery.

Dan Yasaki Which Math? 43 / 45

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Department of Mathematics and Statistics

Reach out to: Sebastian Pauli Tracey Howell Director of Math Pathways Undergraduate Studies Taskforce Co-chair s pauli@uncg.edu thhowell@uncg.edu

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Thank you.

Dan Yasaki Which Math? 45 / 45