maths assignment 02

8/7/2019 Maths Assignment 02

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PRE-SERVICE TEACHERS¶ MATHEMATICAL ENGAGEMENT WITH THE TI-92

(by Monde Mbekwa & Cyril Julie)

Keywords :

Technology ; TI-92 ; Pre-Service Teachers ; Mathematics ; Calculations ; Engagement ; Calculator

1. Introduction :

A very interesting piece of work with bring some food for thought by the writers. The TI-92

calculator is called a ³Super calculator´ by Short (1998) who also described it as a true computer

because of it¶s powerful build-in software capabilities and the QWERTY keyboard at an affordable

price.

According to the two authors of this article, Mbekwa & Julie, the aim of the research was to observe

how technology affected the engagement of teachers with Mathematics. However, the fear of

technology in the classroom by teachers, has been a much debated and discussed topic for quite

some time.

Teachers cannot be blamed for feeling very apprehensive when it comes to the ³unknown´ seeing

that this emotion translates into a lack of confidence which will be noticed by the students . In the

teaching profession, this is the worst what can happen to any teacher as he/she would feel they have

lost a sense of authority (Granger et al

., 2002) and therefore the respect of his/her students.

After reading and analysing the article, there were certain pertinent questions about what Mbekwa

& Julie mentioned as well as the way the research was conducted.

These questions are :

(a) What is the effects of technology in Mathematics ?

(b) Seeing that many English Second Language teachers are teaching Mathematics, how are

Language Barriers influencing the teaching of the subject ?

(c) Because the focus of the article is on a calculator, it would be interesting to see the how the

lack of resources will shape the availability of technology at schools.

(d) What are the various limitations of the TI-92, if any ?

(e) As the sample for this research were pre-service teachers with a low level Mathematics

background, to what extent is Mathematics suffering because of incompetent teachers ?



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2. Main Pionts

Point # 01 : Technology usage in class.

Point # 02 : Exploring Technology in a Second Language

Point # 03 : Mathematics, a scares Commodity

Point # 04 : Incompetency of Mathematics Teachers

Point # 05 : Mathematical Conjecture

3. Summary :

3.1. Views/Findings of Monde Mbekwa & Cyril Julie

This article is about the use of calculators by pre-service teachers in the classroom. Various aspects

were observed by the authors for example, the processes followed by these teachers when given a

calculation or problem to solve as well as the shortcomings of pre-service teachers in terms of using

this kind of technology. One of the issues raised, was the use of ³old technology´, referring to a

pen/pencil and paper, in combination with ³new technology´, the calculator.

The study mentioned that the Home or First language of some of these pre-service teachers, was not

English. Furthermore, the authors state that although certain mistakes were made by these teachers in

the tasks handed to them, it cannot be attributed to the fact that the first language was other than that

of English.

Many of pre-service teachers chosen for this study, had a Low Level Mathematics Experience, which

means that their Mathematical knowledge was limited to Grades 9 and 10 at high school. This wasintentional as the need for Mathematics teachers outstripped the supply. Hence, the study reflected

the reality of what was happening in schools. However, teachers who did not have an interest in the

subject, made instant Mathematics guru¶s.

3.2. My own Views and Opinions of Article :

According to Hawkins, Stancavage, and Dossey (1998) the use of calculators in the classroom will

increase the good achievement by students. This seem to The more competent a learner is pertaining

to the use of a calculator, the more successes the student will attain (Mokros, & Tinker, 1987).

There are still many sceptics when it comes to the use of calculators at school seeing that it will

negatively affect a student¶s Mathematical ability and literacy (Pomerantz, H., 1997). I agree with

this view to a certain extent as calculators, especially at primary school level, must be limited. In my

experience, many learners want to use the tool excessively to an extent where even simple mental

computations, for example 7 x 8 or 19 + 11, is done on it.



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4 . Unknown Words/Expressions :

(a) Imperatives : According to The Free Dictionary means : Important, Extremely Urgent

(b) Algorithms : Wikipedia describes the word as is an effective method expressed as a finite

list [1] of well-defined instructions [2] for calculating a function as shown in Fig 1.

Fig. 1 Flow chart of an algorithm (Euclid's algorithm)

(c) Polynomials : According to purplemath.com, Polynomials are sums of these "variables and

exponents" expressions as portrayed in Fig 2.

Fig. 2 A typical polynomial



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(d) ³ . . . unit of interaction.´ : The website eiu.org, describes the term as actively engaged in

ongoing research into the physical, aural, visual, and gestural interactions between

humans and machines and the various permutations of those interactions.

(e) ³ . . . inductive generalisation . . . ³ : Wiki Answers describes inductive generalization as

when a sample of a population is taken and then a conclusion regarding the entire

population is made. For example, 80% of obs erved mice die when given the drug.

therefore 80% of all mice die when given the drug.

(f) TI-92 : The TI-92 (Table 1) is a graphing calculator which means this handheld calculator is

³of plotting graphs, solving simultaneous equations, and performing numerous other

tasks with variables´ (Wikipedia, 2011). This QWERTY keyboard calculator was

manufactured by Texas Instruments and was introduced in 1995. The TI-92 was the

first calculator with 3D graphing and also came with a computer algebra system or

also known as CAS.

Table 1 : The TI-92 Graphing Calculator

Contrary to the overwhelming good features of the TI-92, there is one major drawback of this ³Super

calculator´ (Short, 1998). This excludes the absents of a backlight which let the user sometimes battle

to get the screen contras right and it¶s bulky size. According to Graham (2003), the one source of

confusion when using the TI-92 for statistical work, it does not distinguish between a symbol whichmust be written as a capital and one written in lower case. This differentiation is important seeing

that certain concepts are encapsulated in symbols. A good example is the symbol sigma, �, when

used in statistics, a Capital � means ³ sum of ´, whereas the lower case symbol , , indicates the

standard deviation.



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This kind of resistance to integrate technology into the curriculum, only exacerbated the digital

divide at an age where even ³grades K-3 are amazingly more technology savvy than many adults

believe, including their parents and teachers´ (NetDay, 2004). This generation is hungry for

anything that has buttons, a screen and most of the time, do what you want it do.

5. Comments :

(a) A calculator can sometimes cause more harm than good In my view, the following is important

to note regarding the use of calculators at Primary school :

(i) A learner must first master certain basic Mathematical skills like counting, addition and

subtraction and multiplication and division prior to the use of the calculators.

(ii) Learners can get too dependent on the calculator where an ³instant´ answer must be found to

a problem. Students must learn that it is human to make mistakes when using mental or

pencil-and-paper computations.

(iii) Many students can get spoiled by this tool to the extend where they get lazy and do not want

spend time to find out the detail behind the calculation.

I am aware that the above-mentioned are made off as myths which are mentioned by Van de

Walle ( 2007) but these are real concerns as a teacher dealing and observing issues happeningin class everyday.

(b) In the article it is stated that technology would be present by 2012 according to the Western

Cape Education Department (WCED). Up till now, it has not materialised as Khanya, which

has been tasked by the WCED will discontinue by 2012 according the Head of Department of

the Western Cape Education Department, Ms Penny Vinjevold ( e4africa, 2011).



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(c) The authors also wrongly assumed that the TI- 92 would be readily available in schools.

Resources, at many schools, are very scares as they have to face many challenges such as

socio- economic conditions and crime on a daily basis. The TI-92, is an expensive Graphing

Calculator in South African terms as the majority of school will not be able to afford it.

However, much cheaper, non scientific and scientific calculators are used currently by school

with great success.

(d) In the observation of the pre-service students, it was found that they tend to first work out the

sum or calculation by hand before confirming the answer on the TI-92. According to me, this

kind of behaviour will decrease as our children in schools are more exposed to technology

where they will feel more at ease using it and also trusting it from the outset.

(e) Another finding is that students did not make use of the resource provided and therefore

constantly requested help from the assistants. It is common that when a person is given a task,

he/she would grab the opportunity if a shorter, easier way can be found to complete it. It

human nature. Contrary to this, it is also human nature to search for answers independently if

no help is provided.If the students were not given assistants to help, in many cases they would

have figure out how to solve the problem with the help of the resources provided.

6. Purpose of Text :

The purpose of the text was to observe how the technology affected the pre-students¶ engagement

with Mathematics. After completing this assignment where I had to read thought this article, I

discovered that a calculator must or can be used more in class and that it is not a crime to let

learners make use of it more frequently when they are experience calculation difficulty. I should see

the calculator as an assistant and not a downfall for the students. They will find Mathematics more

enjoyable as they discover the subject in more depth and gain knowledge at a faster rate.

I shall also allow the learners to solve Mathematical problems on their own as I often tend to jump

in and help without giving them a fair chance of finding the solution themselves. Teachers also

sometimes want things to happen now as they are under great pressure to finish the curriculum in

time. However, providing learners with the necessary resources, they may just surprise us with what

they came up with.



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7 . Conclusion :

A calculator is here to stay and will evolve with time but it¶s role cannot be questioned as it is a

valuable tool in the hands of our learners. Technology will demand a better understanding from us

and it is our duty as teachers to prepare our children adequately as we go into the future. Technology

must be embraced and not be seen as a thread.

maths assignment 02

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