Critical Evaluation of Equivalent Fractions and Multiplication

This discussion post critically evaluates a blog's ideas on teaching equivalent fractions and multiplication, particularly focusing on the use of multiplication as repeated addition. The author agrees with the blog's points on the challenges faced by ELL students and the need to revisit prior grade content in mathematics. However, the author disagrees with using the multiplication model to explain equivalent fractions, arguing that it can be more confusing for students compared to the division model. The post uses examples to illustrate the potential complexity of the multiplication model and suggests that teachers should primarily use the division model for clarity and ease of understanding. The discussion references research on mathematics teaching and learning to support its arguments.

Equivalent Fractions and Multiplication’s Facts
Equivalent Fractions and Multiplication’s Facts
(Blog evaluation)
Institution Name
Student Name

Equivalent Fractions and Multiplication’s Facts
A review of the bog presents several ideas regarding mathematics understanding especially in
equivalent fractions and multiplication. Having analyzed the issues raised keenly, I agree
with a number of facts presented in the blog.
At the beginning the writer indicates that the ELL students have complications understanding
the math’s concepts taught in English. These students originate from nations which do not
speak the English language. Before they can fully learn the English language teachers in the
USA tend to struggle to accommodate them with the other group of students who have
mastered the English language. Another group of students who are almost falling in this
category are students with major deficits. This set of students need to be taught contents
explicitly as any complicated statements by the teacher will put them off. Teaching
mathematics to this group will need a lot of keenness and sensitivity as variations in ideas
presented tend to confuse the students and lower their morale in the subject.
The writer further indicates the need for teachers to dig deep to teach students contents which
they should have covered in the previous grades. This statement can be regarded as a fact.
Mathematics is a continuous subject. Occasionally contents overlap, and students may need
to have understood the previous topics before they can proceed successfully to the next. As
pupils tend to be very forgetful the teacher may occasionally need to go through previous
grade contents before proceeding with the topics in the current grade (Vîrtop, 2016).
One area which the post has given a lot of weight is the understanding of the equivalent
fractions. As the writer has stated, this topic is often confusing. For instance, how do you tell
a student that 2/4 is the same as 12/24. This is a bit complex as the pupil will just look at the
numerators 2 and 12 as well as denominators 4 and 24 and gauge that the cases are different.
In a bid to make students understand this area division model or let’s say simplification of
fractions has been commonly used to explain the case. For instance, in our situation if you
divide both the numerator and the denominator of the second fraction 12/24 by 6 you will
obtain 2/4 to prove that the two fractions are equivalent.
The writer of the post though tried a different approach; using a multiplication model to
explain the equivalent fraction case. This is one area that I disagree with the post. This model
can be very complicated for the pupils to master and they may end up being mix up later
when they come across the mostly used division model. All try to prove this complexity.
Let’s take for instance, the writer has indicated that multiplication is repeated addition. If

Equivalent Fractions and Multiplication’s Facts
you take two fractions 1
2 =10
20 it can be argued that ½ repeats ten times to give 10/20. Then
assume a pupil tries the concept but instead of adhering to the writer's argument that ½
repeats 10 times to give 10/20, he adds 1
2 + 1
2 + 1
2 + 1
2 +1
2 + 1
2 + 1
2 + 1
2 + 1
2 + 1
2 , instead of obtaining
a fraction 10/20 he ends up with 5. To the student he has adhered to the concept of repeated
addition to prove multiplication, but is the eventual answer reflecting equivalent fractions? I
suggest teachers should stick with the division model as it is easier to master and less
confusing (Grouws, 2007).
References
Grouws, J. H. a. D., 2007. The Effects of Classroom Mathematics Teaching on Students' Learning, 1,
Reston VA:, Reston: National Council of Teachers of Mathematics.
Vîrtop, S.-A., 2016. Challenging paradigms in the continuous training of teachers with regard to the
curricular areas of Mathematics and Science. Contemporary Educational Researches Journal, 6(2),
pp. 41-48.