4480 Words May 24th, 2014 18 Pages
Pupils’ Misconceptions in Mathematics
One of the most important findings of mathematics education research carried out in
Britain over the last twenty years has been that all pupils constantly ‘invent’ rules to explain the patterns they see around them.

While many of these invented rules are correct, they may only apply in a limited domain. When pupils systematically use incorrect rules, or use correct rules beyond the their proper domain of application, we have a misconception. For example, many pupils learn early on that a short way to multiply by ten is to ‘add a zero’. But what happens to this rule, and to a child’s understanding, when s/he is required multiply fractions and decimals by ten? Askew
1998).
This approach involves reading 3a + 2b + b + 4a as 3 apples plus 2 bananas plus a banana plus 4 apples, which naturally becomes 7 apples plus 3 bananas or 7a +
3b, which is correct. Unfortunately this would have helped least where I needed help most, and it would also have encouraged the same mistakes!

12

As Doug French points out, if k is interpreted as kangaroos, when faced with the expression 2k + k + 4, the students’ “instinctive thought is likely to be ‘4 what?’. And the obvious answer is 4 kangaroos, giving 7k altogether” (2002: 11).
This is not the only problem that can arise from thinking of letters as representing objects. If a and b represent apples and bananas, then what does ab mean? Indeed, if letters are used in this manner and we are asked to convert the equivalence a week is seven days into a mathematical formula relating days and weeks, we could easily be led to w = 7d rather than d = 7w (where w is the number of weeks, and d the number of days, in a given period).
Given the popularity of the fruit salad approach among teachers at the school in question, I would not be surprised if such a misconception was the underlying cause of much of the confusion on the topic of expanding brackets. However, my experience with the collection of like terms led me to search for other possible explanations for such errors.
My conclusion, confirmed by the literature (Tirosh et

Related Documents

• Essay Benefits Of Using The Cloud System

everything hosted in the cloud is a major component of running a successful business. Amazon Web Services offers a variety of options to host the website, store files, etc., all services Be Well requires in order to operate. Using the cloud as the primary data center is becoming increasingly popular, as many businesses are transitioning from an in-house data center. One reason many people are making the switch is because a cloud system is much cheaper2. In addition, the cloud can be used almost instantaneously…

Words: 1183 - Pages: 5
• Essay Cloud Computing : Using Cloud Storage And Access Of Data

the one mentioned would be incredibly tedious to read. Luckily, this one will not fall into that category, all thanks to cloud computing for allowing essays to be stored & submitted using an online submission system. Cloud computing eliminates the need to keep a tangible copy of information to be shared, allowing storage and access of data simply over the internet. The use of cloud storage is encouraged by many as not only do users put their trust in a consumer agreement, all stored information are…

Words: 736 - Pages: 3
• Essay The Is A Cloud And Fibrous

particles. Nevertheless, we can hold consistently the possibility of something being a cloud and fibrous (47). Subsequently, two predicates such as ‘is a cloud’ or ‘is not a mass of tiny particles in suspension’ refers to one thing while the other predicate does not refer to that same thing (46-47). Similarly, the terms ‘X has a pain’ does not mean the same thing as ‘X has a brain state of pain’. However, both predicates seem logically possible to apply to an object without implying the ontologically…

Words: 1046 - Pages:
• Essay on Cloud

for Multicore and Clouds: Mechanisms and Implementation David Wentzlaff wentzlaf@csail.mit.edu Kevin Modzelewski kmod@csail.mit.edu Charles Gruenwald III Nathan Beckmann cg3@csail.mit.edu beckmann@csail.mit.edu Adam Belay Lamia Youseff lyouseff@csail.mit.edu abelay@csail.mit.edu Jason Miller Anant Agarwal jasonm@csail.mit.edu agarwal@csail.mit.edu Computer Science and Artiﬁcial Intelligence Laboratory Massachusetts Institute of Technology Cambridge, MA 02139 ABSTRACT Cloud computers and multicore…

Words: 786 - Pages: 4
• Essay The Cloud Of Cloud Computing

Abstract— Nowadays, Cloud computing is being the number one concept in IT industry where all large IT companies such as Microsoft, Red hat and Apple are migrating their services to be delivered via the cloud, and through this high competition on cloud-driven services the user is distracted by many different services of different providers which means many different GUIs. Clouds are groups of nodes or machines whose sizes may be different from small machines to data centers [1] [11]. These machines…

Words: 1833 - Pages:
• Cloud Computing Essay

Shall we put our heads in the cloud? A report into the plausibility of investing in cloud computing December 1st 2014 Anonymous student number: Z0942701 Contents…

Words: 4894 - Pages: 20
• Cloud Computing Essay

CLOUD COMPUTING NAME: INSTITUTION: Question 1. What is the most appropriate Cloud Deployment model (or combination) for BPI (Public, Private, Community, or Hybrid)? One of the main things that we need to understand in the process of selecting the appropriate cloud development model for BPI is to understand what cloud deployment is all about. Cloud has been used for a while now and as business and security comes, it is predicted to be rising faster as years come by. The ubiquitous term cloud refers…

Words: 3294 - Pages: 14
• Essay Cloud Computing And The Internet

services over the Internet. This practice has widely come to be known as Cloud Computing. The benefits of such a service are many, but it does come with its own risks. Those who take advantage of such services are exposed to various attacks utilizing the Internet. These potential attacks include, but are not limited to, web browser attacks, Denial of Service (DoS) attacks, and Man-in-the-Middle attacks. In this paper, cloud computing and the three models offered by providers will be defined, then…

Words: 1811 - Pages: 8
• Cloud Computing Essay

Cloud Computing ABSTRACT Cloud computing is Internet- ("cloud-") based development and use of computer technology ("computing"). In concept, it is a paradigm shift whereby details are abstracted from the users who no longer need knowledge of, expertise in, or control over the technology infrastructure "in the cloud" that supports them. Cloud computing describes a new supplement, consumption and delivery model for IT services based on Internet, and it typically…

Words: 1756 - Pages: 8
• Cloud Computing Essay

INFORMATION SYSTEMS III (MODULE B) Databases Call for Term Research Papers Due Date: Thursday 6 September 2012 Cloud Computing Content Page 1. Brief of research project 2. Map of a Cloud Computing 3. Introduction 4. Body 5. Conclusion 6. Bibliography NFORMATION SYSTEMS III (MODULE B) Databases Call for Term Research Papers Due Date: Thursday 6 September 2012 Write a research paper between 1000 – 1500 words on any of the given topics. NO PLAGIARISM WILL BE TOLERATED…

Words: 1302 - Pages: 6