Mathematical Education Thesis 2022

Running head: MATHEMATICAL EDUCATION
MATHEMATICAL EDUCATION
Name of Student
Institution Affiliation

MATHEMATICAL EDUCATION 2
ABSTRACT
This thesis analyses the effects of ongoing evaluation on the self-efficacy of the student
on learning mathematics. The ongoing assessments/evaluations are two where the first one is
homework given to the students. The homework contains ten mathematical questions that are
highly linked to the lecture which has been going on in the classroom. These homework
assignments are on two different levels where the first level is very challenging questions in
which students will have to do lots of revision and consultations while the other level involves
very simple mathematics questions which the students can just answer easily and most of the
concepts are from the lecture notes. The second ongoing assessment involves some small
assessments which contain about 2-3 questions.
These questions are always given to students before the start of lessons every day. The
questions are basically foundation level and can be found in the lecture notes. Thus it will be
very easy for the student who goes through the lecture notes some hours before the mathematics
class since he or she will have a full idea of how the assessment of this type can be handled. The
ongoing assessment has 30 per cent for the formative tests and 70 per cent for chapter test which
makes it a total of 100 per cent. In this thesis, we will deeply analyze the results of the formative
test given to the student, summative tests, mathematics anxiety as well as the learning
environment of these students. In some cases maybe the learning environment can impact on
their performance in mathematics class.
KEYWORDS: Mathematics Self-efficacy, Mathematics Anxiety, Ongoing assessment,
Formative Test and Summative assessment.

MATHEMATICAL EDUCATION 3
TABLE OF CONTENT
Contents
ABSTRACT................................................................................................................... 2
TABLE OF CONTENT.................................................................................................... 3
TABLE OF FIGURES..................................................................................................... 4
LIST OF TABLES.......................................................................................................... 5
CHAPTER 1: INTRODUCTION......................................................................................... 6
CHAPTER 2: LITERATURE REVIEW................................................................................9
Background of self-efficacy on mathematical assessments.......................................................9
Formative assessment.................................................................................................. 13
Example of formative assessment................................................................................ 16
Summative assessment................................................................................................. 17
Mathematics anxiety.................................................................................................... 18
Learning environment.................................................................................................. 20
CHAPTER 3: RESEARCH QUESTIONS............................................................................22
Using the E-class system to facilitate formative assessment can only barely arouse their learning
motivation................................................................................................................. 22
Ongoing assessment improve both mathematics foundation and learning interest.........................25
Can the formative assessment change the learning environment in the classroom.........................26
CHAPTER 4: METHODOLOGY...................................................................................... 28
CHAPTER 5: RESULTS................................................................................................. 29
Results for ongoing assessment improve both mathematics foundation and learning interest...........29
Results Using the E-class system to facilitate formative assessment..........................................40
CHAPTER 6: DISCUSSION............................................................................................ 44
CHAPTER 7: CONCLUSION.......................................................................................... 46
CHAPTER 8: REFERENCES........................................................................................... 49
CHAPTER 9: APPENDICES............................................................................................ 59

MATHEMATICAL EDUCATION 4
TABLE OF FIGURES
Figure 1: Showing some formative assignments given to students ((Hendrickson, 2012)...................13
Figure 2: Showing a graph of the mean score against the number of tens score...............................38
Figure 3: Showing a graph for the mean score of the student learning using I pad on cubes................41
Figure 4: Showing improvement results for the student I pad to learning equations of a line, equation of a
circle, calculus.............................................................................................................. 42
Figure 5: Showing the relationship between the predictor, mediator and dependent variable in learning
mathematics (https://www.sciencedirect.com/science/article/pii/S1041608016301327).....................56
Figure 6: Showing Explanatory sequential mixed methods design
(http://www.tuningjournal.org/article/view/1209/1468)............................................................57
Figure 7: Showing self-efficacy network model (https://link.springer.com/article/10.1007/s11858-017-
0833-0)....................................................................................................................... 58
Figure 8: Showing Model of the impact of academic self-efficacy, approach to learning
(https://www.intechopen.com/books/health-and-academic-achievement/academic-self-efficacy-approach-
to-learning-and-academic-achievement)...............................................................................58
LIST OF TABLES

MATHEMATICAL EDUCATION 5
Table 1: Showing students ́ mean score before the ongoing assessment........................................29
Table 2: Showing students ́ means score after the first ten assessments.........................................30
Table 3: Showing students ́ means score after the second ten assessments.....................................31
Table 4: Showing students ́ means score after the third ten assessments........................................32
Table 5: Showing students ́ means score after the fourth ten assessments......................................33
Table 6: Showing students ́ means score after the fifth ten assessments........................................34
Table 7: Showing students ́ means score after the sixth ten assessments........................................35
Table 8: Showing students ́ means score after the seventh ten assessments....................................36
Table 9: Showing students ́ means score after the seventh ten assessments....................................37
Table 10:mean performance of the students from before conducting ongoing assessments and after a
period of 1 year of conducting ongoing assessments................................................................38
Table 11: Showing improvement results for student learning using I pad on cubes...........................40
Table 12: Showing the results for the student I pad to learning equations of a line, equation of a circle,
calculus....................................................................................................................... 42

MATHEMATICAL EDUCATION 6
CHAPTER 1: INTRODUCTION
It is important to note that student's self-efficacy towards mathematics goes hand in hand
with anxiety. The assessment helps reduce student's anxiety in mathematics which leads to a
positive attitude thus better grades (Akoko, 2011). The role of assessment is to ascertain the
variation in student academic perception and belief in them. It is also meant to point out what
module or approach a teacher should take when handling students. Assessment is meant to point
out student's weaknesses and strengths in various topics in mathematics. It helps in singling out
initial goals and also plays an important role in how the goal is to be carried out to its
completion.
Self-efficacy refers to an individual's confidence in his or her ability. It entails one's view
on one's ability to deal with various circumstances and execute one's goals successfully.
Student's self-efficacy can, therefore, be described as how a student views himself or herself on
how well he or she can overcome and solve various mathematics problems. It is however very
important to note that in whichever way a student views himself (whether he is able or unable)
he or she is right. Assessment leads to a number of things for students. I would start by noting
that a student who has self-assessed himself will tend to give himself a higher grade than the one
a teacher would give him or her. This, in turn, makes a student aim for higher marks in
accordance with the one he assigned himself. A student will, therefore, strive towards hard work
so that he will not be seen to be lower than the grade he gave himself. It, therefore, makes
students have renewed energy most especially when tackling mathematics assignments
(Sriraman, 2011). Therefore it is in order to say that self-assessment leads to improved
performance in mathematics.

MATHEMATICAL EDUCATION 7
The assessment helps in improvement in students learning. This is because students get
motivated to strive even higher. The renewed spirit and energy make them yearn for even more
complex sums. Students, in turn, believe in themselves (Dale H. Schunk, 2012).
It also helps advance student's self-efficacy. This is because assessment helps change the
student's perception of what they viewed and take different approaches. This makes them believe
in themselves thus a reflection of confidence (Jim Campbell, 2012). Through assessment,
students get the ability to exercise control over their motivation. They, therefore, learn to apply
the self-assessment principle in due time. Assessment leads to a teacher having knowledge of his
students. It, therefore, enhances the relationship between a teacher and the students (Bandura,
2011). A student with low efficacy towards mathematics is helped in such a way that their
anxiety towards mathematics is reduced and encouraged on how to embrace mathematics and a
proper way of tackling sums that were previously viewed as difficult (Mathew, 2011).
For my observation, there is a vicious circle for the less able students who come from the
band 2 or band 3 schools in learning mathematics. Compared to band 1's students, their math
learning efficiency is practical lower. Although learning attitude is one of the critical factors,
there must have another deep-rooted reason behind it. I have tried to infer whether self-efficacy
take a role in learning mathematics. I come from a band 2 secondary school, from my experience
I found that the less able students usually don't have motivation in learning mathematics. They
may have several problems in handling the homework's exercises. Since the knowledge of
mathematics is highly coherent between each topic these students lack the motivation to do
revision after school.

MATHEMATICAL EDUCATION 8
Especially for the F4-6 students, they at least have 6 subjects to study under the DSE
curriculum. If they continue the same learning method in junior form, that means just to have a
look of some examples in the textbook before the test or examination, the truth is many students
in band 2 or band 3 are struggling in getting a passing grade in DSE maths examination (Lv.2). If
our students even lose confidence in learning mathematics, how can we expect they can learn
mathematics in a positive attitude? Losing the self-confident in student may result in their poor
performance in mathematics. The above situation is common in many schools. As a local
teacher, it is hard for me to change the exam-oriented system or the syllabus. However, I can
help the students build up the self-efficacy with the tool of assessment. Many mathematics
teachers focus on drilling paper because it is their own so-called successful experience. I am
doubtful about it because not all the students can have the ability to handle the problems. Should
we have some ongoing assessment to help the students to overcome the anxiety of mathematics?
Self-efficacy is simply a perception or a belief that one is able to execute the action
required to succeed at a particular task. Mathematics ability had a direct impact on the
performance of mathematics and also had an indirect impact through a judgment of mathematics
self-efficacy. The judgment of self-efficacy is based on four information sources like the
performance of an individual, physiological state of the student, vicarious experience of
observing the performance of students, Past performance of the student in mathematics test is a
great contributor to the confidence of the student in mathematics tests. In case a student has been
performing well in mathematics then he or she will believe in him or herself and do well. While
for a student who has not been doing so well in mathematics test will have higher anxiety
towards mathematics tests and this will even make him or her to fail more. Such a student may
require vigorous mathematics tests/evaluation to help him do away with mathematics anxiety.