Thoughts on Mathematics 2

Continuation of Mathematics

Author: Manuel R. CortezRodas

The limit of our school year will soon be reached.  The time has come to do an evaluation of the material we have reviewed with our students throughout the year.  This evaluation will allow students to know how their understanding of what they have learned measures in accuracy and competency.  The same evaluation will also allow educators to know how the material they have presented for their students to learn has been understood with both accuracy and competency.  It is important for teachers and students to do a thorough evaluation of the learning that has taken place before the limit of the school year is reached.

Mathematics

Having established a number system, having studied this number system, and having observed the patterns that emerge as numbers in this system are studied, will help us to establish a solid foundation upon which to build our study of mathematics.  With a solid foundation having been established, we can then continue on to the further development of mathematics.  We can begin to apply numeric concepts to help us study and understand from simple to complex systems.

Continuation of Mathematics

The introduction of students to mathematics is covered in three areas: Arithmetic, Algebra, and Geometry.  These three areas are the first building blocks that students should master when they begin to study mathematics.  Students who have demonstrated understanding and can show competency in these three areas should be encouraged to continue their study of mathematics by learning subjects such as Trigonometry, Analysis, Statistics, and Calculus.

Mathematics has the characteristic of reaching across many areas of instruction, fields of study, professional careers, and it is internationally know.  The study of mathematics provides students the skills and abilities to organize their thoughts so they may solve problems that can challenge our lives.  As students are introduced to mathematics, they should also be encouraged to continue the study of this universal, cultural, cross-curricular, multifaceted area of their educational development.

From early on in their educational lives, we as educators should establish an interest in our students to study mathematics.  Our students should be encouraged to continually develop and expand their understanding of the subject areas which make up the subject matter contained in mathematics.  From learning to count with our fingers, to using our fingers for the design and development of tools and machinery, from adding and subtracting to differentiating and approximating, from basic skills to complex interactions, mathematics will forever remain as one of the fundamental areas in our education.

Copyright 2013.  MRCR Educational Consulting Firm.  All Rights Reserved.

Thoughts on Mathematics

Introduction to Mathematics

Author: Manuel R. CortezRodas

We are reaching the limit of our school year, and we must take time to review the material that has been presented to our learners so they may study and learn from it.  Students should have an understanding of the material that we have presented to them this school year.  Students will benefit in their understanding of the material if they are to apply what they have learned, and further develop critical thinking skills based on their education thus far.

Mathematics

Defining mathematics requires the establishment of a number system.  Numbers must be established before we can begin to define mathematics.  Mathematics can be defined at its foundation as the study of numbers.  How numbers are defined, arranged, and the patterns they form.  How numbers interact when performing specific functions and operations, and the results they provide. 

Introduction to Mathematics

Students are introduced to mathematics through instruction in the following three areas: Arithmetic, Algebra, and Geometry.  Arithmetic introduces students to numbers and counting concepts. Algebra introduces students to groupings and operations of arithmetic.  Geometry introduces students to space and dimensions by presenting figures and shapes for study.

Instruction should be presented in a balanced format that allows for presentation by age, grade and skill level.  The measurement of comprehension in mathematics should be measured in the following four areas: Single Problem - Single Solution, Single Problem - Multiple Solutions, Multiple Problems - Single Solution, and Multiple Problems- Multiple Solutions.  Application of the areas that are introduced in mathematics include arts, currency, distance, engineering, science, and time.

We should establish in students an interest in mathematics early on.  We should continue our student's the development of mathematics.  We should expand our student's understanding of mathematics.  We should introduce students to the various specific areas of mathematics, so that they may have a diverse  exposure and understanding of the subject of mathematics.  It is also our responsibility as educators to allow for the exploration and development of mathematical thought in our students, for this will lead to the growth and expansion of the continuation into further mathematics.

Copyright 2013.  MRCR Educational Consulting Firm.  All Rights Reserved.