Calculators for the development of number concept and algebra
My dream of having 80 basic Calculators for my learners was fulfilled on the 3rd November 2005 at 10:00. I prepared a lesson for the Grade 6 class with 47 learners.
At exactly 10a.m the Beyond the Classroom Crew arrived, followed by Ms Yoni Titi from FNB Investments. With formalities out of the way and all protocol observed, the learners were called to come outside to receive the Calculators. There was a lot of excitement as the learners were first given balloons to blow up showing the FNB logo. Ms Titi gave a short speech outlining her involvement with TeachersDream. Then she handed out a calculator and a pen to each learner as they walked back into the classroom.
Ms Titi was then taken aside by the Crew for an interview. I used this time to help the learners to get used to the keys on the calculators we were going to use in the lesson:
On/Clear
Four Operations (emphasis on addition and subtraction)
Equal sign (and the fact that the addition sign also functioned as an equal sign)
I then distributed the worksheets for the lesson on Magic Squares. I was interested to find out how they were going to perform, because we had earlier dealt with the same lesson and some learners had struggled learning a new game whilst managing to add and subtract in order to finish the puzzle quickly.
After Ms Titi’s interview, she and her colleague came to the class and took photos using their digital camera. They gave their last speech and left for the Principal’s office for some refreshments.
Then the lesson began and the Crew filmed every detail, paying special attention to the learners working in pairs on their own. It was encouraging to see the learners who sometimes seem uninterested very much involved, calculating away finding the magic number, all fired up. It was a pretty sight indeed.
We had a break at 11:30 and the Crew was invited to the Principal’s office for some refreshments. The lesson continued again at 11:45. After the lesson, the Crew interviewed me about the lesson and my involvement with TeachersDream. We finished at around 12:30.
Below is a table outlining the progression of calculator skills across the grades. I have highlighted the skills I dealt with in the Grade 6 lesson recorded:
Calculator Skills Focus Areas
Grade 4 Focus
Investigating the number of digits on the display of a calculator
Investigating the keys of a calculator and their functions
Rounding off numbers to the nearest 10
Estimating answers and then finding the actual answers
Reading words off a calculator’s display
Using the constant key to do repeated addition and multiplication on a calculator
Grade 5 Focus
Investigating patterns on the keys of a calculator
Reading words off a calculator’s display
Revising how to correct mistakes on a calculator
Using the constant function to work out the answer
Using rules for the order of operations to work out answers
Grade 6 Focus
Using a calculator to add numbers and to complete magic squares
Investigating how a calculator adds on a constant and multiplies by a constant
Adding a constant to and subtracting a constant from a given number
Estimating answers to addition, subtraction and multiplication calculations
Revising the order of operations
Working with memory keys on a calculator
Grade 7 Focus
Investigating where the different keys are on a calculator
Investigating how the = key operates
Revising how the CLEAR and AC keys work
Revising what happens when one operation is entered immediately after another one
Adding, subtracting, multiplying and dividing by 0 and by 1
Using the calculator’s memory to do calculations
Investigating how the addition, subtraction, multiplication and division constants work
Rounding off numbers in order to estimate answers
Learners were encouraged to define calculator concepts in their own language, thereby articulating the knowledge, values and attitudes.
Learning Outcome 1
The learner is able to recognise, describe and represent numbers and their relationships, and counts, estimates, calculates and checks with competence and confidence in solving problems.
Learning Outcome 2
The learner is able to recognise, describe and represent patterns and relationships, and to solve problems using algebraic language and skills.
Sustainability of the “Dream”
As indicated in the proposal, I am going to use the calculators in my Grade 4, 5, 6 and 7 classes and put them away safely after every lesson. This will ensure that the “dream” lives on for many more years to come. I will continue to encourage learners to use calculators confidently as is required by the learning outcomes.
My aim is to ensure that the learners learn more than just adding, subtracting, multiplying and dividing on a calculator, but to encourage them to ultimately use the calculator as an investigative tool whenever they have to investigate patterns and reach conclusions. Thereby improving their investigative skills.
Challenges anticipated
To discourage the learners from using the calculators as a “crutch”, I will vary the forms of assessment to include written tests in which calculators may be used as well as tests in which problem-solving skills are tested, not just the algorithms and also include tests where the learners will be required to show all their working.
Meaning that I will encourage the use of calculators when working on problem-solving exercises and when dealing with very large numbers. The rest of the time, the learners should use pen and paper methods to find answers. Calculators should in essence be used to enhance the development of mental calculation skills of learners rather than hamper it.
Integration
Calculators illustrate the use of technology in mathematics and serve as a gateway to the use of Computers in problem solving thus linking mathematics with the Technology learning area. Learners need to also realise the development of technology and how it has changed the way people do mathematics now compared to earlier times in human development, thus the link with the Social Science learning area.
Once the learners know how calculators function, they can then use them to perform other calculations wherever required in other learning outcomes within mathematics. I’m referring here to integration within mathematics, for example:
Calculations of percentage increase and decrease,
Data Handling (Pie Graphs calculations)
Decimal Fractions (Conversions)
Calculations of Rate (km/h)
Calculations of Hire Purchase and Interest Rate
Thank you for your generosity and for making my dream come true. With dedicated people like your team, the future of South Africa’s children is in very good hands.
May all your future endeavours be thoroughly blessed!
