Instrumental Relational Perspective

The essay begins with the creation of Algebra in 1545 by doctor Giordano Cardan. It was created to be this way of simplifying problems and Cardan believed it to be an art form that would never go out of style or lose usefulness over time. For the most part he was correct as nearly 500 years later it is still in use, yet for many people it does not simplify anything at all. Cardan was a man of numbers, he gambled and clearly had a great understanding of mathematics, so algebra made sense in his mind but this is not the case for everyone. Math is puzzle that people need to work through to understand, explains Baker, and many people enjoy this aspect of it much like Cardan. Baker himself was a dedicated student who put in week to learn material for a math exam and got a score of 93 for his efforts. Other students, however do not feel as though they can accomplish this. Not all students see the world in numbers and the material they are forced to study is confusing and only gets harder as the course goes on. Fr many student’s algebra

15, via Goos, Geiger & Dole). The dimensions shown in the above paragraph can be considered to be the important areas of real-life use of mathematics, with most use coming from the functional dimension and the critical dimension - which coincide with the Australian Association of Mathematics Teachers’ definition of being numerate. These ideas reinforce each other to paint a picture that numeracy in it’s real-life form is not an exact science, such as copying notes from a board and working through a set of questions, but rather, it is dynamic. To be numerate is to display confidence in mathematics through all sets of skills, even if those skills are not perfectly formed or are lacking in some areas. For example, a hotel receptionist may never use the Pythagoras theorem in her work of booking rooms or her day-to-day life, and thus does not know or have confidence in performing such numerical tasks. Considering she may never use that particular theorem in her life, it would be unfair to describe her as innumerate, as she does not need to display confidence in that area. This example demonstrates the definition of numeracy in terms that backup and demonstrate the concepts provided by Goos, Geiger & Dole, Frogasz, Paige, Lloyd & Charles - as a dynamically suited

2. The authors claim that this book is very different from a typical mathematics textbook. Would you agree or disagree, based on what you read in Chapter 1? Explain.

Mathematical activities at Ysgol Dolafon are delivered in accordance with pupil’s individual needs and great deal of emphasis is given to continuity of learning. Ample opportunity is provided for pupils to discuss their understanding of concepts as they progress and teachers are aware of the importance of eliminating any gaps in the children’s mathematical knowledge. The Welsh Assembly Government guideline for Mathematical Development maintains that: ‘It is crucial that gaps in children’s mathematical learning are avoided, so that children do not miss out on essential elements in their understanding of mathematical concepts’ (WAG 2008) and Ysgol Dolafon fully agrees with that statement.

The general belief around the country (or perhaps even the world) is that math classes will be beneficial to a well rounded student. In some cases, such as the author argued, this might be true as a recent high school graduate who hasn't had the life experiences that someone later in their life might have. The author continues to explain that in their line of previous work and general experience, they already have the general math knowledge that their degree will need.

After doing some research I was able to find a great website that describes this question as it relates many studies. For example,

Geometry and Algebra are so crucial to the development of the world it is taught to every public high school in the United States, around 14.8 million teenagers each year (National Center for Education Statistics). Mathematics is the engine powering our world; our stocks, economy, technology, and science are all based off from math. Math is our universal and definite language “I was especially delighted with the mathematics, on account of the certitude and evidence of their reasonings.” (Rene Descartes, 1637).

The article, “Never Say Anything a Kid Can Say,” by Steven Reinhart, was a very great read and a great article on teaching mathematics in the classroom. The article is about the different teaching techniques that help encourage children in the classroom continuously think about and participate in what they are being taught. I personally enjoyed the article because the techniques that are shared in the article allow the children to experience real life; the children are questioned, allowed struggle, and they are taught they must learn and take responsibility; therefore, this article would be a great addition to the classroom. Steven Reinhart, the author of the article, “Never Say Anything a Kid Can Say,” held a very strong position of basically

The Standards for Mathematical Practice are essential tools that will ensure a student has everything they need to improve in their knowledge and understanding in mathematics. Thus, it is highly important that all level mathematical educators try to implement these standards into their classrooms. Ultimately, there are two sections called, “processes and proficiencies” in which the standards are derived from. The practices are depended on these two standards in the mathematics education. For the reason being, that they provide strategies that will help develop a foundation that students may rely on to comprehend and approach a problem. In other words, the standards do not show step-by-step ways on how to solve a problem, but rather help a student feel comfortable and confident in approaching, analyzing, and finishing a problem. The process standards defined by the National Council of Teachers of Mathematics emphasizes a way of problem solving, reasoning and proof, communication, connections, and representations. The proficiencies identified by the National Research Council include, adaptive reasoning, strategic competence, conceptual understanding, productive disposition, and procedural fluency. Knowing how beneficial the Standards for Mathematical Practice is for students, it is clear that as a future teacher I will implement these strategies in every classroom so that all my students may have a chance to prosper.

Walking into calculus, I was certain that I knew math—I would’ve even gone so far as to say that I understood it. I could memorize formulas and explain proofs, but I couldn’t explain the connections that linked one idea to another. The day Professor Drelles stood before our calculus class with a pair of scissors in one hand and paper in the other, my knowledge turned into understanding. Suddenly, he was an artist, showing us that putting a half twist in a strip of paper and connecting the ends gave the paper a single side. The Möbius Strip: a seemingly simple idea that had complex concepts associated with it.

In today’s society mathematics is a vital part of day-to-day life. No matter what a person is doing at home or at the workplace, he/she is constantly using different mathematics skills to simply function. Then what does this mean for mathematics education? When someone needs to utilize a skill every day then he/she needs a strong background in the skill. Therefore, today’s students need more than a just a working knowledge of mathematics or enough knowledge to pass a test. Today’s students need to understand how mathematics works and how to utilize mathematics skills in the best way possible.

Maths is ubiquitous in our lives, but depending on the learning received as a child it could inspire or frighten. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude toward mathematics as an adult. Solso (2009) explains that math has the ability to confuse, frighten, and frustrate learners of all ages; Math also has the ability to inspire, encourage and achieve. Almost all daily activities include some form of mathematical procedure, whether people are aware of it or not. Possessing a solid learning foundation for math is vital to ensure a lifelong understanding of math. This essay will discuss why it is crucial to develop in children the ability to tackle problems with initiative and confidence (Anghileri, 2006, p. 2) and why mathematics has changed from careful rehearsal of standard procedures to a focus on mathematical thinking and communication to prepare them for the world of tomorrow (Anghileri).

Mathematics, like every creation of man, have evolved without really knowing how far you can get with them: the scope of the computer, physics, chemistry, algebra, all are evidence of this. Every aspect of our culture is based in some way or another in Mathematics: language, music, dance, art, sculpture, architecture, biology, daily life. All these areas of measurements and calculations are accurate. Even in nature, everything follows a precise pattern and a precise order: a flower, a shell, a butterfly, day and night, the seasons. All this makes mathematics essential for human life and they can not be limited only to a matter within the school curriculum; here lies the importance of teaching math in a pleasure, enjoyable and understandable way. Mathematics is an aid to the development of the child and should be seen as an aid to life and not as an obstacle in their lifes.

Mathematics is a challenging subject but of little practical use. Discuss. On account of the initiation of education in human society, Mathematics has taken possession of in the programme of studies. In the recent past, Mathematics is taken to be the foremost subject than ever before (James Lighthill, Newer Uses of Mathematics). The essence of Mathematics is not only meant for skilled or experienced people but also for the common man. Although, Mathematics is the study of numbers or quantity, it has been a crucial tool in our daily life. Like, making purchases, travelling, taxes, insurance all require mathematical calculations. As a consequence, Mathematics is a prime vehicle for the evolution of logical thinking and other professional skills

Mathematics is the one of the most important subjects in our daily life and in most human activities the knowledge of mathematics is important. In the rapidly changing world and in the era of technology, mathematics plays an essential role. To understand the mechanized world and match with the newly developing information technology knowledge in mathematics is vital. Mathematics is the mother of all sciences. Without the knowledge of mathematics, nothing is possible in the world. The world cannot progress without mathematics. Mathematics fulfills most of the human needs related to diverse aspects of everyday life. Mathematics has been accepted as significant element of formal education from ancient period to the present day. Mathematics has a very important role in the classroom not only because of the relevance of the syllabus material, but because of the reasoning processes the student can develop.