StudentShare
Search

# Teaching and Learning Algebra - Essay Example

Summary
Most students find it difficult to understand and apply algebra, especially when first introduced to the subject. This discussion examines some of the reasons for this and focuses specifically on student difficulties with three major algebraic issues…

## Extract of sample "Teaching and Learning Algebra"

Download file to see previous pages According to the report findings if an instructor uses a version of some of these examples, students may be denied a useful frame of reference from the very start of their algebra studies. The last example does relate algebra to arithmetic, a subject which most students will have studied, may know reasonably well and may actually use in their daily lives. But even though algebra and arithmetic both involve signs, equations, numbers and computation, approaching algebra with an arithmetic mindset can cause students major problems.
As the paper declares when introduced to algebra, students must reorient their thinking and recognize that “the expressions on both sides of the equals sign are of the same nature (or structure), and that there are actions which give meaning to the equality of the expressions (for instance, the action of substituting a numerical value for the unknown)”. The process to handle the minus sign before parentheses results in simplifying the expression. Thus, in the above example, 5x – (3 – x) becomes 6x – 3, a more concise and clearer way of restating the original expression without changing its value. In algebra, there is another rule for simplifying expressions, known as combining like terms, which is the third major issue confounding algebra students. Unlike the issues of the equals sign and the minus sign, solving the issue of combining like terms is a matter of following concrete rules rather than grasping concepts. ...Download file to see next pages Read More
Tags
Cite this document
• APA
• MLA
• CHICAGO
(“Teaching and Learning Algebra Essay Example | Topics and Well Written Essays - 1000 words”, n.d.)
Teaching and Learning Algebra Essay Example | Topics and Well Written Essays - 1000 words. Retrieved from https://studentshare.org/education/1566400-teaching-and-learning-of-algebra
(Teaching and Learning Algebra Essay Example | Topics and Well Written Essays - 1000 Words)
Teaching and Learning Algebra Essay Example | Topics and Well Written Essays - 1000 Words. https://studentshare.org/education/1566400-teaching-and-learning-of-algebra.
“Teaching and Learning Algebra Essay Example | Topics and Well Written Essays - 1000 Words”, n.d. https://studentshare.org/education/1566400-teaching-and-learning-of-algebra.
Click to create a comment or rate a document

## CHECK THESE SAMPLES OF Teaching and Learning Algebra

### Seventh Grade Algebra and Learning through Experience

...?Running Head: LEARNING THEORY Seventh Grade Seventh Grade Algebra and Learning through Experience Seventh Grade Algebra and Learning through Experience Introduction The learning outcomes of seventh graders who are given the opportunity to learn algebra are defined by the previous knowledge that each individual has about mathematics. Through understanding Piaget’s theories on learning, it is clear that in order to progress into learning how to do algebra, a student must be able to draw upon what they have learned in the past and how they learned to process the logic of what is being taught. In addition, it is clear that through teaching with the experience of doing, a student will learn at a higher and more comprehensive rate than just...
4 Pages (1000 words) Assignment

### Teaching and Learning Strategies

...Teaching and Learning Strategies: Identifying the characteristics of different teaching Strategies (instruction, demonstration, discussion, Questioning etc) Contents: 1. Using foundations subject a. Role of teacher in showing respect for the diversity of the pupil's social and cultural background in maintaining high expectation for all. 2. Foundation subject: Classroom management and improving the learning climate Reading for research Frame work Developing writing and thinking skills Structured learning Lesson design for attainers Lesson for inclusion...
15 Pages (3750 words) Essay

### Algebra

... algebra, an n-by-n (square) matrix A is called invertible, non-singular, or regular. If an n-by-n matrix exists the matrix must be square. 6) A is expressible as a product of elementary matrices, because every elementary matrices are invertible and its inverse is also an elementary matrices. A square matrix is only invertible if it can be written as a product of an elementary matrix. 7) A family of vectors is linearly independent if none of them can be written as a linear combination of finitely many other vectors in the collection. An alternative method uses the fact that n vectors in Rn are linearly dependent if and only if the determinant of the matrix formed by the vectors is zero. 8) To prove that columns span Rn, finding...
3 Pages (750 words) Essay

### Algebra

...Part I: Linear Algebra and Geometry Assignment: Give a detailed of how linear transformations can be used to study rotated conic sections. Your essay should include: 1) A description of rotations through an angle about the origin. Each of the conic sections which are centered at the origin can be described by the equation Ax2 + Cy2 + Dx + Ey + F = 0 This curve can be rotated through an angle about the origin by using the rotation equations: x = x’ cos - y’ sin y = x’ sin + y’ cos so that the transformation matrix is: R = cos - sin sin cos These values for x and y are substituted into the equation of the curve in order to obtain a new equation for the curve in terms of the x’-y’ coordinates: A’x’2...
4 Pages (1000 words) Essay

### Algebra

...Discussion Evaluating Algebraic Expressions: use the birth or the birth highlighted in yellow Write your birth or the birth someone in your family as mm/dd/yy. (Example: March 13, 1981 is written 3/13/81, and November 7, 1967 is written 11/7/67). 11/2/82 Now let a = the one- or two-digit month number, b = the negative of the one- or two-digit day number, and c = the two-digit year number. (Our example: a = 3, b = -13, and c = 81 or a = 11, b = -7, and c = 67) a = 11, b = 2, c = 82 2. Use the following algebraic expressions for parts c-d of the discussion: 113 – (-2)3 1331 – (-8) 1339 (a-b) (a²+ab+b²) (11 – (-2))(112 + (11*-2) + (-2)2) (11+2)(121 – 22 + 4) (13)(103) 1339 3. Evaluate the three given expressions using the a, b, and c...
4 Pages (1000 words) Essay

### Algebra

Algebra Answer Part Expand along the first row, In terms of symbol the cofactor is, Now, we put all the quantities for the entries. For the cofactors we will put the minor and a (“+1” or a “-1”) which depends on sign required for each minor. This signs will be by going to our “sign matrix” above beginning at the 1st entry in the particular row or column we are expanding along (Larson, & Falvo 110). After that as we move on that column or row we will put the sign required in that case.
Part 2
Expand along the first column,
In this case symbol form of the cofactor is,
Here the signs of “a” are similar to the above case the first row and column have identical signs;
Part 3
In this case we will cofactor expansion a...
1 Pages (250 words) Speech or Presentation

### Teaching architecture, learning architecture

... April Teaching and Learning Architecture from Practice, Memories, and Imagination Architecture is hard to define. In “Teaching Architecture, Learning Architecture,” Peter Zumthor explores the meaning of design to architects. He believes that teachers of architecture only help students answer their own design questions, not offer the right answers. At the same time, teachers learn with their students, as the latter understand what architecture means by doing it. His main argument is that learning architecture involves the intersection of logic, emotion, the senses, memories, practice, and imagination, so that ideas can become tangible expressions. Zumthor asserts that students must learn architecture by using their reason and emotion...
1 Pages (250 words) Assignment

### Teaching and Learning Styles

...﻿Becoming a Teacher I. I was in second year high school when I joined a club that conducted outreach programs to depressed communities. I was assigned in the education team where I tutored some kids from Grades One to Four. The lower levels needed reading sessions while the higher levels required follow up lessons in Math and Science. Most of the kids were eager to attend the classes because they had to complete an attendance record so they could receive gifts at the end of the month and of each year. During my first time of teaching, I observed that kids were jolly despite poverty. They loved to sing and dance to entertain me, and that was how we started our classes. I learned from them the value of fun whilst learning. In the future, I...
19 Pages (4750 words) Assignment

### Teaching learning

...Teaching Learning Within the Kindergarten room of science, the expectations are the to learn mathematics and science. Moreover, they are expected to compute the range and carry out simple science experiments. In the Kindergarten classroom, the teacher strives all the prevailing familiar methods and corresponding strategies, but still encounters a lot of difficulties since the students do not fully adhere to the underlying classroom’s regulations. They execute what they like whilst ignoring what they do not like particularly the male child. In each class day, there is a battle amidst these students. They normally fight within the class for no good reason whilst the teacher is teaching thus disrupting and bothering other prevailing...
1 Pages (250 words) Essay

### Effective Methods of Teaching Anatomy

Herein, comparisons will be made to highlight the differences in using anatomical models for study versus self-directed (usually textbook) learning. As well, the use of tutors as an advantage in the medical classroom will be discussed.

Some students are hands-on learners. For them, three-dimensional (3D) anatomical models are effective. “Exploratory tools enable users to investigate structures in ways not possible in the real world” (Implementing, para. 3). These 3D models can represent just about any part of the human body. Models are available of small structures, like the head, or of the entire human skeleton. Models of the entire human body can also be purchased. Some of them even have removable parts so...
6 Pages (1500 words) Report

### Outlining Explicit Learning Objectives and Outcomes for Teachers and Students

Explicit learning is presented by teaching the specific concepts individually and mastery occurs then after. The main key in such a mode of teaching is being highly structured in every activity that is undertaken inside the classroom can be considered as part of the organization of the technique. One of the defining features of the technique is the fact that the teacher commonly points out the part of the lesson where they are in, thus, the term used is explicit teaching (Boyles, 2002).
The explicit form of teaching can be considered to fit lessons that are considered to introduce certain concepts, ideas or skills that are needed to be learned and that the students have low familiarity or experience with. For that matter, the...
10 Pages (2500 words) Report

### Language Learning Strategies of Listening Comprehension

While some progress has been made during the past decade in establishing more precise definitions and a theoretically based classification system for an LD, it is useful to understand these historical influences because of their continuing impact on diagnostic and treatment practices for children with learning disabilities. The first part of this essay will address the definitional issues, which have molded the field of learning disabilities into its present form, and how to resolve these issues so we can meet the social and educational needs of individuals who display characteristics of learning disabilities. Because LD is often misinterpreted to be synonymous with reading disability or dyslexia, most of the available information...
10 Pages (2500 words) Case Study

### The Constructivist Approach to Teaching Science in the Primary Classroom

When students learn science, they construct meanings and develop understandings in a social context, state Duit & Treagust (1998: 4). Classroom verbal discourse in the form of teacher talk and teacher-student interactions form the basis for most of this meaning-making. Because teacher questions are a frequent component of classroom talk, they play an important role in determining the nature of discourse during science instruction. The cognitive processes that students engage in, as they undertake the process of constructing scientific knowledge, to a large extent depend on the kinds of questions that teachers ask and their way of asking the questions.

Chin (2007: 816) conducted a study to investigate questioning-bas...
7 Pages (1750 words) Case Study

### Teaching Language and Communication Skills

“Language occurs through an interaction among genes (which hold innate tendencies to communicate and be sociable), environment, and the child’s own thinking abilities” (Genishi, 2006). But just how does this happen? How do children learn to use sounds to communicate and then to place those sounds in the correct order to make themselves understood? While some of this behavior can be attributed to the imitation of the caregivers, there remain aspects to the development of language and communication that cannot be so easily explained. To provide a more complete understanding of how language and communication develop in the young child, it is necessary to understand not only the primary terms that are applied, but al...
12 Pages (3000 words) Case Study

### Launch Your Career in College - Learning Agreement

...L E A R N I N G O U T C O M E Assignment Final Learning Agreement with Overview In this section the looks at the sample learning agreement, defines it, describes the breadth component, the depth component, the application component and finally a summary statement noting how the different components are related to one another. The learning agreement that has been provided, gives us an in depth analysis of the student’s personal assessment of his personal strengths and weaknesses, it also states the different opportunities that are available to him and how the student plans to make use of the strengths in a manner that would work to his advantage. Likewise the student has also assessed his personal weaknesses and the threats that can...
7 Pages (1750 words) Assignment

### Developing a Strategy to Enhance Workplace Learning in Workplace at Travelex Foreign Exchange

As earlier stated, I have chosen to answer Option No. 1 which is about drafting and crafting a strategic plan which can be implemented in my workplace as a learning workplace on the basis of its analysis and identification made in the earlier assignments. As also required, the initial paragraph, following this, makes a brief review of what has been done in Assignments 1 and 2. Since as a Training Coordinator, my job entails the induction, training and assessment of the progress of the new hires, I have focused my answer to these three areas and divided the paper into Induction and Training, and; Assessment/Evaluation.

The first assignment was about the physical and social environments of the workplace and in that assign...
8 Pages (2000 words) Assignment

### Learning and Memory Process

...Profile Report This report compares and contrasts the answers provided by the interviewees X and Jason. Learning and memory process Interviewee X prefers to learn by observation and has the ability to give directions to a place that X has earlier visited. Jason also prefers to learn by observation. Interviewee X prefers to work in silence to avoid distraction whereas Jason prefers distractions as they force him to concentrate. Quietude makes his mind wander. Interviewee X’s preference to work in silence points to the use of committing work to the long term memory. Jason displays a preference to utilize short term memory for his work since it has the capacity to focus on the work at hand despite distractions around. The use of short term...
6 Pages (1500 words) Assignment

### Organizational Change is an Opportunity for Organizational Learning

Before we move on to how it is beneficial for everyone, even though it is perceived negatively by a large number of people and is one of their biggest fears, we need to discuss the different kinds of changes and the reason behind them.

An organization can go through a structural change. This can be due to a takeover or a complete change of management. In this type of change, the way of working and many dimensions of business activity is altered. This move is usually towards modernization and staying up with the pace but is too fast and sudden, and thus hard for the stakeholders to adjust with. Then there is a change brought about by the change in the services or goods produced and provided. This is usually a positive ch...
6 Pages (1500 words) Article

### Entrepreneurial Learning

Focusing on those life experiences that actually ‘get in the way’ of entrepreneurial activities, it needs to be stressed that there are several ways in which learning or knowledge that is gained through these experiences affect not only the personality characteristics or traits but predominantly the orientation of people toward engaging in risk-taking and opportunity leverage business behavior. There are actually two ways in which life experiences can refrain individuals from being entrepreneurs; the first way refers to the practical dimension of entrepreneurship whereas the second one refers to the theoretical underpinnings of entrepreneurship (the orientation of the individuals themselves). Within the practical frame...
12 Pages (3000 words) Essay