pamantasan ng lungsod ng maynila (university of the city ... · e) preserve and promote...

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Intended for BS Biology Semester/SY 2nd semester, SY 2014-15

Course Code MMW Course Title Mathematics in the Modern World

Units 3 No. of Hours 54 Contact Hours/Semester

Pre-requisite none Professor(s) Dr. Rebecca C. Tolentino

A. COURSE DESCRIPTION

This course deals with nature of mathematics, appreciation of its practical, intellectual and aesthetic dimensions and application of

mathematical tools in daily life.

The course begins with an introduction to the nature of mathematics as an exploration of patterns in nature and the environment and as an

application of inductive and deductive reasoning. By exploring these topics, students are encouraged to go beyond the typical

understanding of mathematics as merely a set of formulas but as a source of aesthetics in patterns of nature, for example, and as rich

language in itself (and of science) governed by logic and reasoning.

The course then proceeds to survey ways in which mathematics provides a tool for understanding and dealing with various aspects of

present-day living, such as managing personal finances, making social choices appreciating geometric designs, understanding codes used in

data transmission and security, and dividing limited sources fairly. These aspects will provide opportunities for actually doing mathematics

in a broad range of exercises that bring out the various dimensions of mathematics as a way of knowing and test the students’

understanding and capacity. (CMO No.20 series of 2013)

B. UNIVERSITY VISION

Guided by the values of academic excellence, integrity and social responsibility, PLM endeavors to be one of the leading universities in the ASEAN.

PAMANTASAN NG LUNGSOD NG MAYNILA (University of the City of Manila)

Gen. Luna cor Muralla Sts., Intramuros, Manila

6th Flr Gusaling Lacson, Gen. Luna cor. Muralla Sts., Intramuros, Manila5279075

6th Flr Gusaling Lacson, Gen. Luna cor. Muralla Sts., Intramuros, Manila5279075

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C. UNIVERSITY MISSION

The PLM Board of Regents, Management, faculty and staff are committed to: Be recognized by Philippines and ASEAN academic accrediting agencies as a premier university for its quality education, research and extension services Insure that PLM maintains a higher than national average performance on all professional licensure examinations taken by its graduates Continue to provide the students with an education that will give them a competitive advantage from employment oppurtunitiues.

D. COLLEGE OF SCIENCE VISION

We envision the PLM College of Science as the priority choice of students who seek quality undergraduate education, and of a Faculty who actively seek the extension of the frontiers of knowledge through critical study, research and scholarship. The College will likewise be recognized for its role in promoting and upholding sustainable commitment to civic responsibility.

E. COLLEGE OF SCIENCE MISSION

We are a national center for science education instilled with Pamantasan Filipino values. We promote the advancement of knowledge through research and extension services and an encompassing practical application of the same; encourage the achievement of the full academic and personal potential of both students and faculty through scholarly innovations; and uphold unwavering commitment to rise above the challenges of the times. We are steadfast to address the needs of disadvantaged communities through participatory approach.

F. PROGRAM INTENDED LEARNING OUTCOMES (PILOs)

At the end of the program, the students are expected to:

Common to all baccalaureate programs in all types of institutions a) Articulate the latest developments in their specific field of practice. (PQF level 6 descriptor) b) Effectively communicate orally and in writing using both English and Filipino languages. c) Work effectively and independently in multi-disciplinary and multicultural teams. (PQF level 6 descriptor) d) Demonstrate professional, social, and ethical responsibility, especially in practicing intellectual property rights and sustainable

development. e) Preserve and promote "Filipino historical and cultural heritage" (based on RA No. 7722).

Common to the Science and Mathematics Disciplines f) Demonstrate broad and coherent knowledge and understanding in the core areas of physical and natural sciences. g) Apply critical and problem solving skills using the scientific method. h) Interpret relevant scientific data and make judgments that include reflection on relevant scientific and ethical issues. i) Carry out basic mathematical and statistical computations and use appropriate technology in (a) the analysis of data; and (b) in pattern

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recognition, generalization, abstraction, critical analysis and problem solving. j)Communicate information, ideas problems and solutions, both, orally and in writing, to other scientists, decision makers and the public. k) Relate science and mathematics to the other disciplines. I) Design and perform safe and responsible techniques and procedures in laboratory or field practices. m) Critically evaluate input from others. n) Appreciate the limitations and implications of science in everyday life. o) Commit to the integrity of data.

Specific to Bachelor of Science in Biology p) Develop an in-depth understanding of the basic principles governing the science of life; q) Utilize techniques/procedures relevant to biological research work in laboratory or field settings; r) Apply basic mathematical and statistical computations and use of appropriate technologies in the analysis of biological data; s) Extend knowledge and critically assess current views and theories in various areas of the biological sciences

G. COURSE OUTCOME AND RELATIONSHIP TO PROGRAM OUTCOME

COURSE LEARNING OUTCOMES

(CLOs)

PROGRAM INTENDED LEARNING OUTCOMES

At the end of this course, the students should be able to:

a

b

c

d

e

f

g

h

i

j

K

l

m

n

o

p

q

r

s

Discuss and argue about the nature of mathematics, what it is, how it is expressed, represented and used.

Use different types of reasoning to justify statements and arguments made about mathematics and mathematical concepts.

Discuss the language and symbols of mathematics.

Use a variety of statistical tools to process and manage numerical data.

Use mathematics in other areas such as finance , voting, health and medicine, business, environment, art

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and design, and recreation.

Appreciate the nature and uses of mathematics in everyday life.

Affirm honesty and integrity in the application of mathematics to various human endeavors.

H. COURSE CONTENT

DURATION TOPICS LEARNING OUTCOMES TEACHING & LEARNING ACTIVITY

ASSESSMENT METHODS REFERENCES

WEEK 1-2

4 HOURS

Section 1. The Nature of

Mathematics

I. Mathematics in our World Core Idea. Mathematics is a

useful way to think about

nature and our world.

Patterns and Numbers in Nature and the World; the snowflake and honeycomb; tiger’s stripes and hyena’s spots; the sunflower; the snail’s shell, flower petals, world’s population, the weather etc.

The Fibonacci Sequence

Mathematics helps organize patterns and regularities in the world.

Mathematics helps predict the behavior of nature and

1. Identify patterns in nature and regularities in the world (K)

2. Articulate the importance of mathematics in one’s life (V)

3. Argue about the nature of mathematics, what it is, how it is expressed, represented and used (K)

4. Express appreciation for mathematics as a human endeavor (V)

Activities to do. (i) video

watching (ii) pair-sharing

or small group sharing (iii)

journal writing (iv) whole

class discussion

Questions to Pose (i) What

is Mathematics? (ii) Where

is Mathematics? (iii) What

role does mathematics

paly in your world?

Some ideas to elicit and

encourage. (i) Many

patterns and occurrences

exist in nature, in our

world, in our life.

Mathematics helps makes

Evaluation Requirements. (i)

short-response/essay writing at

the end of class to one question.

Examples of these questions

are: what new ideas about

mathematics did you learn?;

what is it about mathematics

that might have changes your

thoughts about it?, and; what is

most useful about mathematics

for humankind? (ii) Two-to-

three-page synthesis paper

focusing on one of the following

aspects of mathematics: (a)

Mathematics helps organize

patterns and regularities in the

world. (b) Mathematics helps

predict the behavior of nature

and phenomena in the world. (c)

Mathematics helps control

nature and occurrences in the

world for our own ends.

Required: (i)

Nature’s

Numbers by Ian

Stewart or

Mathematics in

Nature:

Modelling

Patterns in the

Natural World by

John A. Adam or

A Mathematical

Nature Walk by

John A. Adam or

any book of the

same level,

intent and

approach (2)

https://vimeo.co

https://vimeo.com/9953368

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phenomena in the world.

Mathematics helps control nature and occurrences in the world for our own ends.

Mathematics has numerous applications in the world making it indispensible.

sense of these patterns

and occurrences. (ii)

Mathematics is a tool to

quantify, organize, and

control our world, predict

phenomena, and make life

easier to us.

Some ideas to discourage

or debunk or disprove.

(i)Mathematics is just for

the books, confined in the

classroom. (ii)

Mathematics has no place

in my life.

Standards/Basis for Grading to

Use. 0 point – The student is

unable to elicit the ideas and

concepts from the readings and

video indicating that s/he has

not read the prescribed reading

or watched the video.

1 point – The student is able to

elicit the ideas and concept

from the readings and video but

shows erroneous understanding

of these.

2 points – The student is able to

elicit the ideas and concept

from the readings and video and

shows correct understanding of

these.

3 points – the student not only

elicits the correct ideas from the

readings and video but also

shows evidence of internalizing

these.

4 points – The student elicits

the correct ideas from the

readings and video, shows

evidence of internalizing these

and consistency contributes

additional thoughts to the Core

idea.

m/9953368

Recommended:

(1) A Day’s

Adventure in

Math

Wonderland by

Akiyama & Ruiz

(2) The number

Devil by

Enzensberger

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Week 2-3

3 hours

Section 1. The Nature of

Mathematics

II. Mathematical Language and Symbols

Core Idea. Like any

language, mathematics has

its own symbols, syntax and

rules.

Characteristics of mathematical language: precise, concise, powerful

Expression vs. sentences

Conventions in the mathematical language

Four basic concepts: sets, functions, relations, binary operations

Elementary logic: connectives quantifiers, negation, variables

Formality .

Activities to do.(i)

Individual or small group

exercises including

games (see exercises in

The Language of

Mathematics(from One

Mathematical Cat,

Please! By Carol Burns

Fisher) (ii) Whole class

discussions of the

comparisons between

the English and

Mathematical language

(iii) Compilation of

mathematical symbols

and notations and their

meanings


encourage.

(i) Mathematics is a

language in itself.

Hence, it is useful in

communicating

important ideas. (

(ii) ii) Mathematics as a

language is clear and

objective. (iii) Language

conventions are

Evaluation Requirements, (i)

Writing exercise sets (ii) Quiz

Standards/Basis for Grading to

Use. Use numerical scores.

Required for

Instructors;

Jamison, R. E.

(2000). Learning

the language of

mathematics.

Language and

Learning across

the Disciplines,

4(1), 45-54.

(attached)

Required for

Students: (i) The

Language of

Mathematics

(from One

Mathematical

Cat, Please! By

Carol Burns

Fisher) (ii) The

Language and

Grammar of

Mathematics

(both attached)

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necessary in

mathematics for it to

be understood by all.


or debunk or disprove. (i)

Mathematics is not a

language but a useless

set of formal rules and

alien symbols. (ii)

Mathematics confuses

the communication of

concepts and ideas. (iii)

Mathematics is full of

unnecessary symbols,

rules and conventions.

Week 3-4

5 hours

Section 1. The Nature of Mathematics III. Problem Solving and

Reasoning Core Idea. Mathematics is

not just about numbers;

much of it is problem

solving and reasoning.

Inductive and Deductive Reasoning

Intuition, proof and certainty



7. Argue about the nature of mathematics, what it is, how it is expressed, represented and used (K)

8. Express appreciation for mathematics as a

Activities to do. (i) reading

and writing proofs (ii)

small-group problem

solving (iii) whole class

discussions of key

problems and solutions


encourage. (i)

Evaluation Requirements.

One (1) take-home

problem set

Standards/Basis for

Grading to Use. 0 point –

The students did not make

any attempt to solve any

of the problems in the

Required: Mathematical Excursions (Ch. 1) by R. Aufmann et al.; What is Mathematics Really? (Ch.4&5) by R. Hersh;

Recommended:

Mathematical

8

Polya’s 4-steps in Problem Solving

Problem solving strategies

Mathematical Problems involving Patterns

Recreational Problems using mathematics

human endeavor (V) Mathematics requires not

only facility with numbers

but also the ability to

critically think through

situations, to reason and

argue logically and to

creatively solve problems.

(ii) Mathematics is an

active human endeavor.

We can create the

mathematics we need to

solve problems. (iii)

Mathematics is for

everyone and anyone who

cares to learn it. (iv)

Mathematical problem

solving takes time.

Solutions are not always

apparent to the solver. (v)

There may be more than

one approach in solving

mathematical problems.


or debunk or disprove. (i)

One only needs to learn

numbers and fractions to

be mathematically

proficient (ii) Mathematics

problem set or prove any

of the statements in the

quiz. 1 point – The student

attempted to solve 50% of

the problems in the

problem set or displayed

logical reasoning 50% of

the time in attempting to

prove the statement/s in

the quiz. 2 points – The

student attempted to

solve all the problems in

the problem set or

displayed logical reasoning

75% of the time in

attempting to prove that

statement/s in the quiz. 3

points – The student is

able to completely solve

50% of the problems in

the problems set or

completed 75% of the

problems in the problem

set or completed all the

proof/s in the quiz.

Excursions (Ch.2)

by R. Aufmann et

al.; Mathematics,

A Practical

Odyssey (Ch.1)

by Johnson &

Mowry; The

Number Devil by

Enzensberger,

Professor

Stewart’s

Cabinet of

Mathematical

Curiosities by Ian

Stewart;

Problem Solving

Through

Recreational

Mathematics by

Averbach and

Chein.

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is a spector sport.

Mathematics is just out

there to be discovered and

appreciated. (iii)

Mathematics is for the

gifted. (iv) One is dumb if

s/he cannot solve a

mathematical problem

right away. (v) There is

only one way to solve a

mathematical problem.

Week 5-8

10 hours

Section 2. Mathematics as a

Tool (Part 1)

Data Management

Core Idea. Statistical tools

derived from mathematics

are useful in processing and

managing numerical data in

order to describe a

phenomenon and predict

values.

Review: Descriptive Statistics, Normal Distribution, Hypothesis Testing, Regression and Correlation (Chapter 1, 5, 8 & 9)

Activities to do. (i) lectures

(ii) work with appropriate

computer statistical

software, like Excel (iii)

class discussions

Examples of applications.

1. A brisk walk at 6.4 km/hr burns an average of 300 calories per hour. If the standard deviation of the distribution is 8 calories, find the probability that a person who walks 1

Evaluation requirements.

(i) 1 quiz (ii) group project

proposal for a quantitative

study

Sample Project Proposal

You want the university to

offer free shuttle rides for

students, faculty and staff

from strategic points

outside your university in

order to improve traffic

flow in your campus. The

university chancellor asks

your team to present hard

Required: CK-12

Probability and

Statistics

Advanced

Second Edition

(pdf file)

Recommended:

Mathematics, A

practical

Odyssey by

Johnson &

Mowry (Ch.4)

10

Chi-Square (Chapter 10)

Planning or Conducting an Experiment or Study (Chapter 6)

Note: (i) The topics to be

reviewed are expected to have

been covered in Junior and Senior

High School. The focus should

then be on deepening and using

these to be able to critically

examine information from various

sources (e.g. newspapers). (ii)

Exert efforts to use technology

that are available to students.

hour at the rate of 6.4 km/hr will burn the given number of calories. Assume the variable is normally distributed. (a) more than 280 calories (b) less than 293 calories (c) Between 285 and 320 calories (From: Sobecki et al., Math in Our World). Interpret the result for each number of calories.

2. Does good health relate to education? Below are the figures for the Philippines: Immunizzation (measles, % of children ages 12-23 months) 2005…92 2006…92 2007…92 2008…92 2009…88 2010…80 Primary completion rate (total, % of relevant age group) 2005…94 2006…91

data that will convince the

administration. Prepare a

proposal on how you will

do this task.

Standards/Basis for

Grading to Use. (i)

Numerical scors for the

quizzes, test and problem

sets (ii) rubric for the

project proposal

Caution. (i) Define the

bounds of the project

proposal to ensure that

the work required is

commensurate to the

hours allotted for this

section of the course. (ii)

The oral proposal is not to

be graded.

Math in Our

World by

Sobecki, Bluman,

& Schirck-

Matthews

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2007…91 2008…92 2009…91 2010…no data

Can you predict the

primary completion

rate for 2010?

WEEK 9-

11

10 hrs

LOGIC

Logic statement nd

quantifiers

Truth tables and

tautologies

Conditional, biconditional

and related statements

Symbolic arguments

Aeguments and Euler

diagrams

9. Use mathematical

tools in logic

Activities..(i) lectures (ii)

role playing (iii) written

exercises


(i) 1 problem set (ii) an

integrating project

Week 12-

14

10 hrs

III. The Mathematics of Graphs

Graphs and Euler circuits

Weighted Graphs

Euler’s formula

Graph coloring



12. Argue about the

Activities..(i) lectures (ii)

role playing (iii) written

exercises


(i) 1 problem set (ii) an

integrating project

Sample Integrating Project

(by groups)

Johnson &

Mowry, Ch. 12

Aufmann et al.,

Chapter 11

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Week

15-17

12 hrs

IV. The Mathematics of Graphs

Graphs and Euler circuits

Weighted Graphs

Euler’s formula

Graph coloring

nature of mathematics, what it is, how it is expressed, represented and used (K)

13. Express appreciation for mathematics as a human endeavor (V)

Create a poster aimed at

recruiting students to join

a club that promotes

mathematics as an

important tool in everyday

life.

Standards/Basis for

Grading to Use.(i)

Numerical scores for

problem sets (ii) Rubrics

for the project

Aufmann et al.,

Chapter 5

I. GRADING SYSTEM

Midterm exam – 20% Final exam - 20% Quizzes - 30% Assignment/Project - 15% Seat Work/Recitation - 10% Attendance/Behavior - 5% Total 100% Passing percentage – 60%

Grading Scale

98-100 ....................................... 1.00 83-85 ............... 2.25

95-97 ......................................... 1.25 80-82 ............... 2.50

92-94 ......................................... 1.50 77-78 ............... 2.75

89-91 ......................................... 1.75 75-76 ............... 3.00

86-88 ......................................... 2.00 <75 .................. 5.00

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J. COURSE AND CLASS POLICIES

ATTENDANCE

Attendance will be checked anytime during the first 30 minutes of the class sessions. Any student who is not in class when attendance is checked will be marked “ABSENT”. When the total number of hours lost by absences exceeds 20% of the class hours, the student will be automatically dropped from the subject. For this course, a student’s absence should not exceed 8 meetings. Excuse slips must be presented to the instructor not later than the second session of the class after the date of the student’s return.

Seat works, Assignments and Recitations

From time to time, seat works shall be given. During these exercises, students may be allowed to open their own notes but borrowings of calculator and notes are not allowed . Answers to assignments should be written in yellow pad and/or graphing papers and will be checked during class sessions. All recitations will be graded accordingly. Take note that no make-up will be given for any work covered by the class during the absence, either excused or unexcused.

Long Exams

Excused absences during an examination will be dealt with on a case to case basis. However, an exam missed due to an unexcused absence

is equivalent to a grade of zero on that activity.

pamantasan ng lungsod ng maynila (university of the city ... · e) preserve and promote...

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