Mathematics in the Ateneo

Senior High School

Philippine Association of Colleges and Universities

November 24, 2016

Republic Act 10533

Enhanced Basic Education

Act of 2012

Fermat’s Last Theorem

• No nonzero solution for these

3 3 3a b c

4 4 4a b c

when 3n n na b c n

• Many possible solutions for this

2 2 2a b c

PythagoreanTheorem

• San Lorenzo Ruiz was beatified-1981 and was

canonized-1987

• FLT was proved by Andrew Wiles-1995

What is one thing that is common to both

San Lorenzo Ruiz and Fermat’s Last Theorem?

• San Lorenzo Ruiz was martyred on 1637.

• FLT was conjectured on 1637.

“Mas madaling maging santo kaysa mag-solve ng Math problems.”

“It is easier to do God’s work than to solve Math problems.”

When Am I Going to Use This?!?!

I Never Used Math in My Life!

Abraham Wald

1902-1950

I Never Used Math in My Life!

Math SAVES Lives! Abraham Wald

1902-1950

“Put the armors on the parts

that weren’t hit.”

I Never Used Math in My Life!

2. Again, Math SAVES Lives!

From JOSE:

2 boxes of apples

3 boxes of oranges

I Never Used Math in My Life!

From PEPE:

1 box of apples

6 boxes of oranges

Then I have

3 boxes of apples

9 boxes of oranges

From PEPE:

1 box of apples

6 boxes of oranges

I Never Used Math in My Life!

From JOSE:

2 boxes of apples

3 boxes of oranges

Then I have

3 boxes of apples

9 boxes of oranges

3. I have an apple, then I have

algebra.

Of course you will place your bet on the

black card.

I Never Used Math in My Life!

4. Math WINS a game!

SHS Mathematics 1. (Core) General Mathematics

2. (Core) Statistics and Probability

3. (Specialized) Pre-Calculus

4. (Specialized) Basic Calculus

frequency of the sessions!

schedule of long tests!

schedule of semestral subjects!

SHS Mathematics

Suggested STEM Math Schedule

SHS Mathematics 1. (Core) General Mathematics

2. (Core) Statistics and Probability

3. (Specialized) Pre-Calculus

4. (Specialized) Basic Calculus

frequency of the sessions!

schedule of long tests!

schedule of semestral subjects!

Ateneo SHS Practices

Regular Team Meetings

Ateneo SHS Practices

Formal and Random PLCs

Ateneo SHS Practices

Study Halls

Ateneo SHS Practices

Technology

Technology in Math

Education

CONCEPTUAL FRAMEWORK

The specific skills and processes to be developed are: knowing and

understanding; estimating, computing and solving; visualizing and

modeling; representing and communicating; conjecturing, reasoning,

proving and decision-making; and applying and connecting.

…conjecturing…

We recognize that the use of appropriate tools is necessary in teaching

mathematics. These include: manipulative objects, measuring devices,

calculators and computers, smart phones and tablet PCs, and the

Internet.

NCTM Position

It is essential that teachers and students have regular access to

technologies that support and advance mathematical sense making,

reasoning, problem solving, and communication. Effective teachers

optimize the potential of technology to develop students’

understanding, stimulate their interest, and increase their

proficiency in mathematics. When teachers use technology

strategically, they can provide greater access to mathematics for all

students.

Technology in AHS

• GSP

• Graphmatica

• Graphing Calculator (Casio fx-9960G)

• Geogebra

• Autograph

• Graphing Board

• Edmodo

• EDU 2.0

• Desmos

• Wolfram Alpha

• Schoology by Rexdigital

Disadvantages

• Mathematics requires quite a bit of practice at

problem-solving. Technology cannot solely take

the place of good ol’ fashion paper and pencil with

certain elements of mathematics. Roblyer and Doering (2013)

• Students tend to think and consider that having

technology during a summative test will be very

reliable for them. Students tend to become

complacent.

Disadvantages

• Students who are exposed to using of technology

have poor writing skills.

• Possible disconnect of social interaction.

• Students do not have equal access to technological

resources.

Disadvantages

• The quality of research and sources they find may

not be top-notch.

• Lesson planning can become more labor intensive

with technology.

Advantages Our goal is to teach mathematics so that people see it as useful, and see it as something with which they can solve problems, and technology can help us to do that.

• Technology has the ability to bring the intangible

and abstract to life. (Roblyer & Doering, 2013, p. 310)

(Example1) (Example 2)

• Another advantage of using technology in math is

that it is “more student-centered, active, and

relevant to the world we live in” (Roblyer & Doering,

2013, p. 310)

Gives opportunity for investigation or exploration

(Example)

Advantages • The integration of technology in mathematics

continues to build higher cognitive problem

solving, logic, and reasoning skills. (Example)

• The Geometer’s Sketchpad® is the world’s leading

software for teaching

mathematics. Sketchpad® gives students at all

levels—from third grade through college—a

tangible, visual way to learn mathematics that

increases their engagement, understanding, and

achievement. Make math more meaningful and

memorable using Sketchpad. http://www.keycurriculum.com/

(Example)

Advantages

(Technology Elements for PS)

In 1852 student Francis Guthrie notices that four colors suffice to color a map of the countries of England. From 1879 up to the 20th Century many attempts of proving and disproving the conjecture happened but none was successful. In 1997, a proof was finally published by Robertson, Sanders, Seymour, and Thomas but greatly relied on a supercomputer that exhausted all the possible cases.

Useful tools for PS and exploration

• Arithmetic computation tool

• Graphing tool

• Spreadsheet/MS Excel (Example)

• Interactive geometry

Advantages

(Technology Elements for PS)

More advanced tools

• Computer algebra systems

• Interactive mathematics software, e.g. Geogebra,

Autograph, Cabri, GSP, etc.

• Virtual manipulatives

• Web tools e.g. Googlemaps

Technology in Math Education

Our [Teachers’] goal is to teach mathematics so that people see it as useful, and see it as something with which they can solve problems, and technology can help us to do that.

Curriculum Issues in an Era of Common Core State Standards for Mathematics by Zbiek and Heid

Ateneo SHS Practices Worksheets

Ateneo SHS Practices Problem Sets

Ateneo SHS Practices Test Modifications

Ateneo SHS Practices All tied to our Ignatian Pedagogical

Paradigm (IPP).

I Never Used Math in My Life!

Math teaches to solve some problems

by pattern finding.

Thank you!