Math Pre-Assessment Part 1: Exponents, Reflection, and Implementation

This assignment presents a pre-assessment designed for 8th-grade students struggling with exponents, focusing on conceptual understanding and addressing confidence issues. The assessment involves a detailed explanation of exponent rules, including multiplication and different bases. The student reflects on the pre-assessment, incorporating feedback from a mentor teacher. The feedback emphasizes the need for more interactive activities, a focus on student engagement, and the integration of ICT resources and dialogic teaching methods. The reflection also discusses challenges in identifying engaging activities and the importance of considering student input. References include works by Alexander (2008) and Kunska & Savicka (2012).

Math Pre-Assessment
Part 1: Pre-Assessment and Implementation
Grade level of mentor class: 8
Standards being taught in mentor class:
Description of unit being taught in mentor class: Factorization of numbers, multiplication,
Division, Fraction Rules.
150-200 word description of Pre-assessment:
This pre-assessment is targeted towards those students who perform poorly in the class
because of limited conceptual knowledge and lack of confidence about asking queries becauie
of peer pressure. Here the primary focus is on understanding exponents in mathematics. The
key question that is being focused on is why, during multiplication, different exponents for the
same base are added while different bases for the same exponent are multiplied with the
exponent common.
In order to do that, the students who are in the identified weakly developed zone are brought
together and given a brief about the concept of exponent and powers. The pre assessment
session starts with providing the students a general recap about exponents where the students
identify that the exponents are basically the number of times the base number is multiplied by
itself. So if the base number is 3 and the exponent is 4, it means that 3 is multiplied by 3, four
times.
3 4 = 3 x 3 x 3 x 3 = 81
Afterwards, the teacher will write on the board the following equation:
2 3 x 3 3 ……… (a)
Here the teacher will expand the equation as follows:
(2 x 2 x 2) x (3 x 3 x 3)
= (8 x 27)
216.
Alternately, on the other side, the teacher will write:
216 = 6 x 6 x 6
= 6 3
= (2 x 3) 3 ………. (b)
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Once the teacher had written this information, s/he will highlight that the equation given at the
beginning (a) can therefore be written down in the form of (b). That is to say that for same
exponents, the base can be multiplied. However the practical implication for this breakdown
comes when a bigger base with an exponent needs to be identified.
In the second section, the teacher will write the following equation:
2 3 x 2 5 ………… (c)
Here the teacher will use the same principle for breaking down:
(2 x 2 x 2) x (2 x 2 x 2 x 2 x 2)
= 8 x 32
= 256
= 2 8
= 2 (3 + 5)
Here the teacher will highlight how, with the same base, the exponents are added.
At the testing phase, the teacher will provide similar examples for the students to test and the
accuracy of the results will be determined by the correctness of the response and how
effectively the students have been able to come to that response.
Feedback from mentor teacher:
I see that you have provided quite an elaborate but fairly simple example for explaining
exponents to your students. I can also see why this is easier to understand. If the students are
not very good at manual calculations, you can use a calculator in the class or use the help of an
online video, like a source from YouTube, to develop digital literacy (ICT) outcomes on the
side as well.
Going back to your pre-assessment, I see that the activity does not have much student
engagement. The results need not be discussed, but for the sake of your students’
understanding, try to give more simple examples for the students to solve first. Once the
students have understood the calculation bit of it and had grown confident about the theory,
make them focus on the equations and how they need to be broken down. You mention that
the students have issues with confidence, yet your pre-assessment does not clearly address that
point in the activity. Try to make the activity more discussion based instead of pedantic. Try
looking at the concept of Alexander’s dialogic classroom and understand how the concept of
exploratory talk in the classroom has been promoted (talk plays a crucial role in the classroom
to develop conceptual knowledge, despite common preconceptions of talk being disruptive).
Include that as a part of your pre-assessment and you are all set to go.
Part 2: Reflection
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Reflecting on my field experience, I can state that the selecting the students was fairly
simpler. Once a few students were identified, I was able to identify the rest from their peer
group, because social learning theory dictates that the individuals (adolescents in the current
context) act in accordance with the normative behavior of the group that they belong to.
Therefore, in their peer group, most of the students were lacking general conceptual knowledge.
Firstly, I was able to understand that the pre – assessment activity was not appropriately
following the particular teaching standards. It needs to be more interactive as the mentor
feedback suggested. Therefore, that is one aspect that I need to take care of in my teaching.
Besides that the second aspect that I need to take care of is the appropriateness of the content that
I was dealing with. The students are particularly poor in understanding the concept of exponents,
because they are not used to asking queries in the class for their personal academic development.
Therefore, they are weak in these particular areas and need special conceptual scaffolding from
the teacher.
Finally I was also able to understand that the incorporation of ICT based resources in the
task was an important factor that needed analysis and evaluation (Kunska & Savika, 2012). ICT
plays an important role in helping the students pay more attention in the class and understand the
concepts better. I can use an iPad or a computer and also play YouTube videos that will help
them understand the nuances of the concept. As the mentor feedback highlighted, I also need to
look at Alexander’s (2008) dialogic classroom to promote communication amongst the students
for this activity. This helps develop confidence and the students will be able to ask questions in
the class that will help them gain a stronger understanding of the relevant concepts.
This pre-assessment activity has challenged me in terms of devising ways that I can use
to help the students identify their weak areas and build up on them. The most challenging part
was the identification of appropriate engaging activities for the students. Here I need to focus
more and be more creative, as well as consider the students’ inputs.
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References.
Alexander, R. J. (2008). Towards dialogic teaching: Rethinking classroom talk. York: Dialogos.
Cunska, A., & Savicka, I. (2012). Use of ICT teaching-learning methods make school math
blossom. Procedia-Social and Behavioral Sciences, 69, 1481-1488.
© 2018 Grand Canyon University. All Rights Reserved.