Contrasting Relational Understanding And Instrumental Understanding

2059 words - 8 pages

Introduction
In 1976 Skemp published an important discussion paper spelling out the differences between relational and instrumental understanding as they apply to mathematical teaching and learning. Skemp highlights two faux amis, the first is understanding. Skemp defines understanding in two ways: 1) instrumental understanding and 2) relational understanding. The second faux amis is the word mathematics which he describes as two different subjects being taught. I have considered Skemp’s article in four sections.
1. Faux amis
2. Instrumental and relational understanding
3. The mismatch
4. Implication for mathematics teaching
Key terms: Schema; faux amis; Instrumental understanding; relational understanding; mathematics.
Setting the Scene
It is extremely difficult to define understanding. Skemp attempts to assimilate it into some form of an appropriate or inappropriate schema that is dependent upon many variables such as language, environment, belief, tradition and culture. Could understanding be an abstract thing, brain pattern or rule? Skemp uses the term ‘faux amis’ to mean that language can have different meanings to different people even though the root origins of words are the same. He looks at French and English and identifies what he calls a ‘mismatch’. He uses analogies and understandings based on his own experience and others in his community of practice (Mellin-Olsen, 1981). This mismatch, he believed, is the root of many difficulties in mathematics education including the word mathematics itself. This assignment attempts to appraise his arguments in relation to other literature and my own personal experience.
A schema is a mental structure we use to organize and simplify our knowledge of the world around us. We have schemas about ourselves, other people, mechanical devices, food, and in fact almost everything. Skemp uses the notion that different mathematical ideas are seen as objects and processes for an individual to encapsulate into some form of schema. It is argued that schema theory lacks a consistent definition and it has its roots in idealist epistemology and mixed empirical studies (Sadoski, 1991).

Instrumental understanding is where you apply an appropriate remembered rule to the solution of a problem without knowing why the rule worked. Instrumental understanding can be seen in terms of tacit content knowledge of the methods of mathematics. Tacit meaning it is difficult to transfer the knowledge by means of writing it down and is therefore communicated somehow to the student. Gregory Chaitin, a mathematician and computer scientist argued that understanding something means being able to figure out a simple set of rules that explains it (Chaitin, 2006). In teaching directed numbers and rationalising the denominator as a remembered rule is much easier than trying to get students to identify with the concept relationally. In my experience as a teacher certain pupil’s go through their mathematics education at...

Find Another Essay On Contrasting Relational Understanding and Instrumental Understanding

Productive communication and understanding Essay

572 words - 2 pages MODULE 2 ESSAY 1 2MODULE 2 ESSAY 1 4Module 2 Essay 1 Aspen UniversityCOM100: Introduction to CommunicationsJuly 21, 2014Running head: MODULE 2 ESSAY 1 1Module 2 Essay 1Understanding others is an integral aspect of effective communication. Learning to communicate productively entails having knowledge of some barriers to understanding. Cultural differences can hinder communication if they clash. In some cases, beliefs and thoughts of a different

Productive Communication And Understanding Essay

716 words - 3 pages MODULE 2 ESSAY 1 2MODULE 2 ESSAY 1 4Module 2 Essay 1 Aspen UniversityCOM100: Introduction to CommunicationsJuly 21, 2014Running head: MODULE 2 ESSAY 1 1Module 2 Essay 1Understanding others is an integral aspect of effective communication. Learning to communicate productively entails having knowledge of some barriers to understanding. Cultural differences can hinder communication if they clash. In some cases, beliefs and thoughts of a different

UNDERSTANDING LANGUAGE AND LITERACY

1149 words - 5 pages address different levels of social situations. Academic literature expands the first knowledge of literacy into a more sophisticated way of using language. It aims to allow students to actively participate of community life through understanding and creating literature. Academic literature covers reading, writing, comprehension, note taking, and the ability to hold an argument, communication and team and work planning. Academic literature is

Understanding and Defining Sustainability

800 words - 3 pages Understanding and Defining Sustainability In your own words describe what you understand what is meant by sustainability. The Cambridge Advanced Learner's Dictionary definition of sustainability is - 'causing little or no damage to the environment and therefore able to continue for a long time'. My view of sustainability when concerned with the manufacture of products is that during manufacture, the materials

Developing and Understanding Worldviews

1061 words - 5 pages Charles Colson. The company was founded in 1939, by Herman Baker. The company has published many Christian books that discuss many issues such as family life and theology. Baker Academic serves the academy and the church by publishing works that further the pursuit of knowledge and understanding within the context of Christian faith. “Building on our Reformed and evangelical heritage, we connect authors and readers across the broader academic

Understanding and Overcoming ADHD

1580 words - 6 pages teacher is often the first one to suggest a test for ADHD. "Teachers can be your best allies if you have ADHD." (Beal 35) Students with ADHD may need their teachers' understanding, cooperation, and classroom accommodations in order to do their best."If you have ADHD, it's a good idea to make an appointment with all your teachers at the beginning of each school year."(Beal 36) Talk to the teacher about your disability. With some teachers you can make a

Understanding and Developing

1376 words - 6 pages the favorite age group because the child is getting taller, filling out, and learning many new things. During the cognitive domain a child develops their memory, grasps new concepts, and makes decisions. Jean Piaget’s theory would be more equip for the cognitive domain. Piaget studied a child’s development of understanding by observing and talking to them, and managed to come up with four stages of cognitive development: sensorimotor from birth

Defining and Understanding Stress

2263 words - 9 pages Defining and Understanding Stress According to the www.oxforddictionaries.com stress is defines as a state of mental or emotional strain or tension resulting from adverse or demanding circumstances. Stress is a feeling created when we react to particular event such as bad work place, traffic jammed, break up, too many assignments and many more other sample. Stress rise our mental and body to a challenge and preparing to meet a tough situation

Understanding Correlation and Causality

2193 words - 9 pages kids by itself will cause one to gain weight. Conclusion It is important to understand how researchers and writers come up with conclusions on causality. While there are many variables that can show correlation, the idea that a change in one variable triggers a change in another variable is harder to validate. Therefore, understanding where the data came from, interpreting it for its’ correlation coefficient, and running additional tests, will help

Understanding ADD and ADHD

3533 words - 14 pages Understanding ADD and ADHD First, it is important to understand ADD and ADHD and how they can be identified. Within the classroom, a teacher may encounter a student who constantly squirms in their seat, stares out the window, and has a desk that is a complete mess. These are not poor students who do not care about school and learning. Often these students may be undiagnosed cases of Attention Deficit Disorder or Attention Deficit

The Bible and Understanding Scripture

962 words - 4 pages The Bible and Understanding Scripture The Bible is God’s word to His people. Christians are taught to read and study the Bible daily. A new person in the body of Christ would understand reading and studying just as one reads a regular book or study material. Often Christians are not taught how to read and study, instead they internalize reading and studying as memorization of the Bible because most Christians can remember the word of God

Similar Essays

The Setting Is Instrumental To The Understanding Of Characters In Wuthering Heights

1200 words - 5 pages The setting of Wuthering Heights is instrumental to the readers understanding of the characters by conveying ideas of their attitudes and emotions which are tied to different places throughout the novel. The story is anchored and atmosphere is created by the setting. Wuthering Heights is set on the Yorkshire moors in the 18th century. The moors are the basic setting in which Bronte begins to establish the lonely atmosphere which

Audience Understanding And Understanding Someone Else's' Audience

1692 words - 7 pages , lifestyle, goals, and beliefs. Other ways to obtain information about your audience, is through other presenters, (if there are any,) as well as, inquiring and understanding the overall expectations of you. The type of venue also indicates information about the audience, is it at a school, a hotel, or perhaps an office complex. Preferably you can preview the venue before your interaction, either days before or hours. The interaction and dress code

Peace And Understanding Essay

1027 words - 5 pages delivers unto the mind, heart and soul a flow of unique inertia and insight. Momentum to seek out things that surpass your own understanding, whilst cradling your own perception of what is and what is not. In this context, we can contextualize this version of peace as that which “surpasses all understanding.” This innate aspect of Buddhism finds itself nestled in the foundation of “Nirvana.” However, “what Nirvana is” and “how it applies to our reality

Explanation, Understanding, And Subjectivity Essay

3302 words - 13 pages Explanation, Understanding, and Subjectivity ABSTRACT: Many theorists of explanation from Hempel onward have worked with the explicit or implicit assumption that considerations of the subjective sense of understanding should be kept out of the formulation of a proper theory of explanation. They claim that genuine understanding of an event comes only from being in an appropriate cognitive relation to the true explanation of that event. I