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TMN3704 Assignment 02 (Teaching Mathematics in the Intermediate Phase)
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STUDENT NUMBER: 62191411SUBJECT: TMN3704
ASSIGNMENT 02
UNIQUE NO.: 534490
SEMESTER: 01
DUE DATE: 19 JUNE 2020
, QUESTION 1:
Standard Algorithms VS Student-invented Strategies
A standard algorithm is a step-by-step method, while student-invented
strategies are methods produced by learners themselves, for a better
understanding.
Student-invented strategies exist, because learners tend to think of problems in
different ways than the “normal” way in which they were taught. Traditional
algorithms look at a number as a whole, whereas student-invented strategies
look at the number, beginning with the largest part. This means that learners
can be flexible with the problems instead of just seeing the problem how it is in
the traditional sense.
Students are able to solve problems mentally with the use of invented
strategies, which goes beyond just computing answers as in the traditional way
when making use of standard algorithms.
Students tend to make fewer errors when using invented strategies, as long as
they understand the methods that they use and can make sense of it.
A benefit of using student-invented strategies is that the teacher wouldn’t have
to do a lot of re-teaching than when using traditional methods.
Invented strategies – when clearly understood – can be used repeatedly by the
learner, whereas in traditional ways, the teacher may have to re-teach the
strategies often.
Students are able to make sense of the numbers they use when making use of
student-invented strategies and are able to explain their work. Traditional ways
make use of rules which can be much harder for the learner to understand and
make sense of.
1 STUDENT NO.: 62191411
, QUESTION 2:
Writing 2-digit numbers in connection with the base-10 meaning of ones and
tens.
When children count, they learn the numbers as a kind of “continuum” that just
goes on and on…
They might not initially understand that our number system has an inherent
structure that’s based on groups of tens, hundreds, thousands, etc.
A good way to have a child understand this concept is to have the child count a
large number of items in groups. (e.g. counting in groups of 2, 5, 10, etc.)
Another way to have children form a better understanding is by giving them
large numbers and have the learners add them together using the group
system, for example:
51 + 28 =
Place them under each other according to groups. Units under units and tens
under tens. And write them out in expanded notation.
tens units
5 1
2 8
(50 + 1) + (20 + 8) =
Explain that only those from the same group can be added together.
Tens (50 + 20) and units (8 + 1).
50 + 20 = 70
8+1=9
Explain the concept of placeholders.
0 is a placeholder for 9.
The total isn’t 709, it’s 79.
tens units
7 9
2 STUDENT NO.: 62191411
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