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.

STEAM Education Lessons

Introduction to STEAM Education Lessons

Author: Manuel R. CortezRodas

What is a STEAM education lesson?

A lesson is a prepared presentation on an educational topic that is based on the principal strands of STEAM education.  The presentation that is prepared as a STEAM education  lesson should present information in the best educational format that allows for the students of the lesson to best learn the STEAM educational topic.

What is the objective of a STEAM education lesson?

The objective of the STEAM education lesson should be for the students to learn the educational topic of the lesson.  The educator can reach the objective by presenting the lesson by using one or a combination of various methods like lectures, textbooks and resources, research and projects, video and audio clips, letters, experiments and demonstrations, field trips, assignments, homework, guest speakers, and many more.

How is the success of a STEAM education lesson measured?

The success of the STEAM education lesson can be measured using a variety of scales and tools, however, once the measure for success has been established, it must be implemented uniformly to the students as a whole.  The measurement of success must also be fair and balanced, and allow, with in a reasonable time frame, for the possibility of reaching success by ways of reevaluation and/or reassessment.

How is a STEAM education lesson implemented?

The implementation of a STEAM education lesson is to be decided by the creator of the lesson, or the educator who has been trained on how to present such lesson.  When implementing a STEAM lesson, the following factors should be taken into consideration: the students, the classroom, knowledge level, supplies and materials, age, grade, learning skills and abilities of those whom we expect to be learning the STEAM lesson that is presented.

 

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

Language & Communication: Writing

"Language and Communication"

"Writing"

Author: Manuel R. CortezRodas

Defining Writing

Writing is a tactile visual form of communication.  When we write we create a visual communication that can be sensed by touch.  Writing requires that we imprint onto, a tactile material, representations for thoughts and ideas.  Writing is developed through our ability to make marks and leave imprints by using the tools and materials available to us from our current technology. 

When to be Writing

With growth and training we begin to recognize lines, curves, and shapes that we try to replicate by carving, drawing, and inscribing. We use our fingers and hands before moving onto pencils and markers.  We mold clay, chisel rock, and carve wood.  We add our own creative style when replicating letters by creating fonts, adding color, underlining, and making bold traces.  We should encourage each other to develop writing skills from the earliest possible time in our life.

How much writing is good

Although we have established measuring units for writing like words, sentences, paragraphs, pages and essays, we should also keep in mind that we must look at what is being communicated to us through the writing.  Words should be spelled correctly, sentences should be complete, paragraphs should be thorough, essays should be structured properly so that the thoughts and ideas that we are going to convene through writing are clear.

Why should we be writing?

Writing provides for us a concrete record of thoughts, ideas, and expressions.  If the writing is done by many people, with a purpose, after careful consideration of worries and concerns, then writing can become a long lasting example of not only literal meaning, but of a reflection of the human characteristics of thinking, cooperation, development, and growth.  Writing allows us to reach others and share opinions, and if it lasts through time, writing allows us to reach future generations, as well as allowing them to look back at past ones.

Copyright 2012. MRCR Educational Consulting Firm. All Rights Reserved.