Mathematics is the universal language

Mathematics is...

a universal language that describes the natural world, allows communication

between languages and cultures, and teaches the ability to think sequentially

ASSESMENT:

Assembling evidence from a variety of assessment strategies

is a routine part of the mathematics classroom

and assists in forming an accurate picture of

an individual student’s progress toward

learning goals. Data gathered from

assessments is used to inform

instruction.

  Communication

Mathematics instruction pro-vides opportunities for students

to effectively communicate their mathematical thinking, orally and

in written form, to peers, teachers, and others by using the precise

language of mathematics. Through communication, students evaluate their

own mathematical thinking as well as analyze the strategies of others

Conceptual Understanding

Teachers provide sufficient time and experiences which enable

students to actively build new knowledge from prior knowledge

so that understanding deepens and the ability to apply math-

ematics in new situations expands. Conceptual understanding

supports retention and prevents common errors. 

Connections

Mathematics represents a network of interconnected concepts

and procedures. Connections are made within the same mathematical structure,

 between mathematical strands, and to other  disciplines and daily living.

Cooperative Learning

Cooperative learning offers students opportunities to explore and discuss

challenging problems which would normally be beyond the capacity of an individual.

This creates opportunities for students to discover and test conjectures based

upon mathematical principles. Through  working together, students increase

self-confidence, deepen mathematical understanding, and utilize social skills.

Multiple Representations

Students should create, select, and apply various representations to organize,

record, communicate, and prove mathematical ideas. These representations may include

diagrams, tables, graphs, symbolic expressions, and physical models. Representations should

 support students’ understanding of mathematical concepts and relationships.

Experiences with concrete models followed by pictorial representations assist in developing abstract thinking.

Problem-Solving

Knowledge is built through the solving of problems that arise

in mathematics and in real world contexts. Students use

and adapt a variety of strategies that enable them to monitor

and reflect on mathematical processes. The teacher’s role

is crucial in choosing appropriate problems that encourage

students to explore, take risks, share failures and successes,

and question one another.

Technology

Technology plays an increasingly important role, helping the

current generation of students visualize and learn mathemat-

ics. While technology should not be used as a replacement

for basic understanding and computational proficiency, mul-

tiple forms of technology used properly in the mathematics

classroom can deepen students’ understanding of mathematical concepts

 When technology is placed in the hands of students, attitudes toward

mathematics are improved, allowing focus on decision making

 reflection, reasoning and problem-solving, while also preparing students for 21st

century life and careers.

Parent Involvement

Parents play a critical role in a child’s math achievement.

Parents need to support students in developing an attitude

that effort, more than natural talent, leads to increased stu-

dent achievement. Changing children’s beliefs from a focus

on ability to a focus on effort increases their engagement in

mathematics learning.

Prime numbers

•       Remember how the early scientists visited Africa and some other parts of the world and ‘discovered’ naturally existing things like mountains, rivers and other places, something close to that has happened again.

•      This time round, though, it is not in either of the above areas.

•      Two mathematicians have uncovered a simple, yet previously unnoticed quality of prime numbers. So, apparently, the prime number sequence isn’t as random as earlier thought.

• Prime numbers as you will hopefully recall from your early formation years in primary school, are whole numbers that are only divisible by 1 and themselves. They include 2,3,5,7,11and so on.

•       In a paper by researchers studying the primes at Stanford University, the prime numbers, it seems, are trying very hard not to be similar.

•       Kannan Soundararajan and Robert Lemke Oliver, present new evidence that prime numbers ward off other would-be primes that end in the same digits.

via GIPHY

•      From the initial set (numbers less than ten) 2 and 5 were part of the primes, but when they appear next as in 12, 15, 22, 25, they are no longer primes as they are divisible by other numbers other than 1, and themselves. Thus, all other prime numbers can only end in one of four digits: 1, 3, 7, or 9.

•       Armed with the fact that prime numbers appear to be random, or so it was thought, the pair of mathematicians decided to test this ‘randomness’ assumption on primes. They discovered a strange phenomenon entrenched among the integers that prove there’s certainly an un-random pattern at play.

•             If they were truly random as earlier thought, primes ending in 1 would be followed by a prime ending in 1 about 25% of the time. However, the mathematicians found this order occurred in only 18.5 percent of cases.

• It was discovered that a prime number was followed by a prime ending in 3 or 7 was about 30 percent of the time and about 22 percent for 9.

•            Although their study is yet to checked and approved by experts before it can be officially published in a peer-reviewed journal, the study has received a lot of attention from other mathematicians.

•           As fascinating as the new study appears, George Dvorsky in an article argues that it likely won’t help with other prime-related challenges including the twin-prime conjecture or the Riemann hypothesis. He adds that the new discovery may not have any practical implications or use to math and number theory.