Effectiveness
The difference between effectiveness and efficiency can be stated as follows: "Effectiveness is doing the right things, and efficiency is doing the things right".
The effectiveness of maths software depends on a number of measurable factors, the first of which is the conformance to the syllabus. It does not help if the teacher is trying to teach the reading of a protractor, and software only asks for the estimate of an angle. In order to evaluate the conformance to the syllabus, it is essential to actually work with the system.
Secondly, it is necessary to study how the system can be tailored to student capability. It is extremely important to have the ability to apply remediation on the spot where a student with difficulty is identified. In the same vein, it should be very easy to extend the stronger student by placing him into more advanced work, without disturbing the discipline in the class.
Lastly, it is necessary to study the methods so that a student in difficulty is identified.
Efficiency
The efficiency of maths software relates to the adherence of maths principles and is more difficult to measure. Every program needs to be evaluated carefully, to study the "learning experience" to be gained from using it. For example, look at the addition of decimal numbers.
The better systems would request the child to write the decimal numbers below each other before the addition is done. The learning experience gained in this instance is to line up the numbers below each other around the decimal point. In weaker systems, the numbers are placed below each other by the computer, allowing the child only to add the numbers. The problem is therefore reduced to become a normal problem of addition and the learning experience becomes zero.
Furthermore, some systems accentuate accuracy of operations to the detriment of speed by forcing the student to redo the problem until he eventually gets it right. The better systems accentuate accuracy as well as speed, by allowing the child freedom of errors, but to re-test him at a later stage in the learning process. In other words, it is better to do 200 problems in a half hour, of which maybe 20 are wrong, than to do 50 in a half hour, all correct, because the student was given two to three chances to rectify the mistakes.
In short, the efficiency of the maths software relates to the strength of the foundation that is built at each level of the learning experience.
The learning process and cognitive overload
For learning to take place, learners must acquire skills, attitudes or knowledge that they did not previously have. These end products of the learning process are called outcomes. All the activities, approaches and assessment methods that are used in the classroom should be directed at achieving the relevant outcomes for that level.
Learning something is accomplished by creating that something. A major part of learning goes into creating bare new concepts in the working memory of the student. This creative process is dependent upon the knowledge stored in long-term memory and the capacity of the working memory of the student. The capacity of long-term memory is vast and one of the skills in learning something is to develop enough |
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understanding of subject matter to enable it to be stored in long-term memory.
In contrast to this, short-term memory is limited and the student processes all the unknown facts and variables in this limited workspace while attempts are made to create new concepts. This working memory is also used only for a short period of time and the images therein last only long enough to complete a certain task. If the short-term memory cannot process all the information it is confronted with, cognitive overload occurs.
Students struggling with mathematics are a direct result of cognitive overload. Mathematics is an incremental subject, where the knowledge created during one year and committed to long-term memory is drawn upon in subsequent years.
Many things may have happened in the classroom, such as a long-term illness, unavailability of teachers or more interest in extra-curricular activities to have prevented the long-term memory from acquiring the necessary knowledge. The student now has to grapple with so many imponderables at the same time in his working memory, that it soon leads to a failed solution attempt. Any factor that increases the cognitive load is likely to interfere with learning.
Drill & Practice
The time-honoured teaching format of drill and practice for mathematics learning is still used widely. There is no question that if student A has done three times as many problems as student B that he is likely to react with automaticity when similar problems are seen again. What has happened is that more of the long-term memory was developed which leads to higher confidence levels and less likely cognitive overloading. Drill and practice exercises on paper have fallen into disfavour, because of the high workloads placed upon the teacher in setting the exercises and in marking them. The drill and practice methodology has one good attribute - a low cognitive loading.
Worked examples
The next higher level of cognitive loading is the studying of numerous worked examples. If it is used in conjunction with a drill and practice method, it can draw on the dependencies stored in long-term memory and a symbiotic relationship can be created, with significant esults. Used on its own, however, it can place a much higher cognitive load on the student as the methods used by experienced tutors sometimes skip many interleaving steps.
Constructivism
A popular method of teaching mathematics is currently based on the concept of investigative mathematics. Students are given tasks, based around concrete problems, and are encouraged to seek outcomes from group discussions. Unfortunately, by allowing the learner to create his own methods freely and openly, the initial guidance work for the teacher becomes enormous. This workload is reduced considerably as the learner becomes a more complex, self-organising person.
This openness is very important to creativity and thus learning. All forms of closure, irrespective of how minute it may be, quenches creativity and thus degrades learning to some extent. Obviously, memorisation of a complex answer is the worst form of closure. It may be considered learning by certain individuals, but it has very little value. The brighter quick-thinking students bloom in this free form, open-ended style of teaching but the slower students find the cognitive overload overwhelming.
The use of computer technology
Over a period of 10 years of development, a leading new programming style has resulted, that allows the students to create new concepts at every level in an open-ended mathematics system. Thus incorporating all methods of effective learning.
Developing confidence
By self-creating the concepts to be mastered, the learner acquires the necessary potential energy to attempt an even higher order of learning. This energy is usually known as confidence or motivation. There is no other way to acquire that potential energy. Lack of this potential energy leads to a non-spontaneous state. Resultantly the teacher needs to force the student to learn. As soon as the teacher stops, the learning stops.
The solution was therefore to use a blend of the three methodologies described above in conjunction with a few other facilities. At the heart of the system, you still need a good, solid drill and practice program. The computer removes the boredom of traditional paper-based D & P systems as it can literally generate thousands of different questions. Constant monitoring applying the software in such a fashion that cognitive overload does not occur and as soon as mastery on one level is demonstrated, the learner automatically progresses to a higher level of work.
Secondly, the graphics capabilities of the programme is used to highlight the problem areas with multicoloured dynamic sketches, again increasing the understanding of subject matter and reducing cognitive overload. The system developed does not use the passive studying of worked examples, but includes a dynamic, interactive tutorial, where the next step is suggested through active prompts. It allows for neater, clearer screen layouts without any intrusive and uncalled for help systems.
Thirdly, a critical requirement for education is to have continuous assessment. Learners are assessed continuously whilst using the programme. CAMI uses two assessment systems: a quantitative marking system to evaluate the accuracy of working plus a time based evaluation to measure the work rate of the learners. This type of assessment is both learner-paced and learner-centred to ensure that it fulfils both the developmental and monitoring functions.
Benefits
Why are so many schools in the world using CAMI for their numeracy training?
Because it produces RESULTS, and it does so QUICKLY
CAMIˇ®s unique instructional technology excites, motivates and challenges students of all ages and levels. Combining the latest teaching theories and computer capabilities, the entire system promotes an understanding of important critical thinking skills. The developers are active mathematics specialists who have been successfully teaching the full spectrum of school mathematics since 1984. Many thousands of students have benefited from having worked on the CAMI system.
Why does the CAMI system work so well?
CAMI software makes use of modern technology. Development started in 1984 in the CAMI mathematics school and several programming philosophies were tried over the years before a new event-driven programming style was chosen. Using CAI (Computer Aided Instruction) programming techniques, the efficiency of the CAMI system was trebled during 10 years of research and development.
The system is used for diagnosis, practice and remediation and helps the student to understand and solve real life problems. The programs are highly interactive, provide reinforcement of all concepts and are flexible enough to allow simultaneous access to a wide range of different problems.
CAMI is DIAGNOSTIC - Students are placed in their exercises where the progress is monitored continuously. Individual reports, printed on demand, analyze the results and highlights problem areas.
CAMI provides PRACTICE - Drill and practice exercises are given to each student on the exact level that needs reinforcement. The activities feature a wide range of exercises and provide practice and review in mental computation, logic and problem solving. Students work at their own pace. Most of the programs include three or more progressive levels of difficulty.
CAMI is FLEXIBLE –The learner is in control of the learning process No pre-programming of paths, breakpoints or levels of difficulty is required. The program can be interrupted at any stage and scores will be automatically stored for all work done to that point.
The MANAGEMENT – The system is completely automatic. It records studentˇ®ˇ®s progress, from which you can obtain individual scores, a summary of scores or a printout of the summary for all the diagnostic results by simply making easy selections on a menu. |
