Mathematics

BEST PRACTICES IN MATHEMATICS

INTRODUCTION

              Mathematics is a form of reasoning. Thinking mathematically consists of thinking in a logical manner, formulating and testing conjectures, making sense of things, and forming and justifying judgments, inferences, and conclusions. We demonstrate mathematical behavior when we recognize and describe patterns, construct physical and conceptual models of phenomena, create symbol systems to help us represent, manipulate, and reflect on ideas, and invent procedures to solve problems. 

DEFINITION of 'BEST PRACTICES'

              A best practice is a technique or methodology that, through experience and research, has proven to reliably lead to a desired result. A commitment to using the best practices in any field is a commitment to using all the knowledge and technology at one's disposal to ensure success. The term is used frequently in the fields of health care, government administration, the education system,hardwareand software product development, and elsewhere.

             A best practice is an industry-wide agreement that standardizes the most efficient and effective way to accomplish a a desired outcome. A best practice generally consists of a technique, method, or process. The concept implies that if an organization follows best practices, a delivered outcome with minimal problems or complications will be ensured. Best practices are often used for benchmarking and represent an outcome of repeated and contextual user actions.

               Concurrently, the following best practices for implementing effective standards-based math lessons should be followed:

• Students’ engagement is at a high level.
• Tasks are built on students’ prior knowledge.
• Scaffolding takes place, making connections to concepts, procedures, and understanding.
• High-level performance is modeled.
• Students are expected to explain thinking and meaning.
• Students self-monitor their progress.
• Appropriate amount of time is devoted to tasks.

ORIGIN OF SUDOKU

                           The great mathematician Leonhard Euler is the man chiefly credited with the creation of the puzzle that we now know as Sudoku. Born in Basle, Switzerland in 1707 just after the giant leap forward in mathematics pioneered by Isaac Newtonand Gottfried Leibnizhe both consolidated and pioneered mathematical knowledge in many fruitful areas. He moved from Basle to St Petersburg, Russia to study medicine but by the chance happenings of fate he became the chief mathematician at the St Petersburg Academy . In 1741 he spent 25 years in Germany before returning to the Academy in Russia where he died at the grand age of 76. Even though blind for the last seventeen years of his life he still made important discoveries.

Hypersudoku

                          Hypersudoku is one of the most popular variants. It is published by newspapers and magazines around the world and is also known as "NRC Sudoku", "Windoku", "Hyper-Sudoku", and "4 Square Sudoku". The layout is identical to a normal Sudoku, but with additional interior squares defined in which the numbers 1 to 9 must appear. The solving algorithm is slightly different from the normal Sudoku puzzles because of the emphasis on the overlapping squares. This overlap gives the player more information to logically reduce the possibilities in the remaining squares. The approach to playing is similar to Sudoku but with possibly more emphasis on scanning the squares and overlap rather than columns and rows.

HOW TO SOLVE SUDOKU PUZZLES QUICKLY AND RELIABLE

               For many who are new to Sudoku puzzles, finding a solution can be a complete mystery. On one hand, with so many numbers, Sudoku seems very mathematical. On the other hand, without the appropriate solution techniques, it can amount to a lot of guessing and checking.

In truth, Sudoku puzzles are very well structured and predictable – much like mathematics.

Before we cover how to solve Sudoku puzzles, let’s take a moment to review a few aspects of Sudoku including the rules, terminology, and game variations.

What is Sudoku?

A Sudoku puzzle is defined as a logic-based, number-placement puzzle. The objective is to fill a 9×9 grid with digits in such a way that each column, each row, and each of the nine 3×3 grids that make up the larger 9×9 grid contains all of the digits from 1 to 9. Each Sudoku puzzle begins with some cells filled in. The player uses these seed numbers as a launching point toward finding the unique solution.

It is important to stress the fact that no number from 1 to 9 can be repeated in any row or column (although, the can be repeated along the diagonals).

There are many variations on Sudoku including Mini Sudoku, Cross Sums Sudoku, Killer Sudoku, and Wordoku. We will not cover such variations here.

While solving Sudoku puzzles can be significant challenge, the rules for traditional solution finding are quite straight forward:

Each row, column, and nonet can contain each number (typically 1 to 9) exactly once.

The sum of all numbers in any nonet, row, or column must match the small number printed in its corner. For traditional Sudoku puzzles featuring the numbers 1 to 9, this sum is equal to 45.

This is an important point to review as it isn’t uncommon for inexperienced players to get frustrated and to abandon the techniques we will lay out below. Don’t do it! In order to solve Sudoku puzzles reliably, you must be disciplined, focused, and patient.

    There are two main techniques one can use to solve a Sudoku puzzle; Crosshatching and Penciling In. These two techniques are simple, straightforward, reliable, and sufficient in solving most standard Sudoku puzzles.

      It is important to understand that all Sudoku puzzles require an iterative approach. Except for in the case of the simplest puzzles, players will have to visit each nonet more than one time. Fortunately, each successive application of the solution techniques yields more completed cells.