Integrating Ancient
Egyptian
Mathematics in
Teaching
Partial Fractions
through
Lesson Study
Authors:
CRUZ, Erika April
DY, Audric Curtis
ESPANOLA, Melchor
JUSTIMBASTE, Brenda
PERALTA, Henry
REYES, Still John
VILLANUEVA, Abigael
ELIPANE, Levi
Science Education
Department
De La Salle University –
Manila, Philippines
• Insert pictures of the lesson study
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
INTRODUCTION
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
OBJECTIVES
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
• To integrate History of Mathematics (Ancient
Egyptian Math) in teaching partial fractions.
• To determine how history of mathematics
could be an effective pedagogical tool in
improving mathematics teaching and learning
processes.
• To increase student’s interest.
• To improve the lesson plan and the lesson
itself through lesson study.
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
CONCEPTUAL FRAMEWORK
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
• Using the integration of the history of
mathematics into classroom instruction as
pedagogy in mathematics (Weng Kin Ho, 2007).
• Lesson Study (LS) is an emerging model of
continuing professional development for teachers
that is school-based and teacher-led (Ulep, 2013).
• Productive pedagogies (intellectual quality,
connectedness, supportive classroom
environment, and recognition of difference) can
make an impact to students’ academic and social
outcome from schooling (Lingard et.al., 2001).
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
METHODOLOGY
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Participants
• Fifteen 4th year high
school students (boys
and girls) from School
of Everlasting Pearl,
Inc., in Antipolo, Rizal,
Philippines.
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Observers
• Six teachers from
School of Everlasting
Pearl Inc.
• Students from De La
Salle University –
Manila taking Masters
of Science in Teaching
Mathematics.
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Lesson Plan
• Big Idea (Yo! Break it down!)
• Overarching Question (How do you
decompose a fraction?)
• Part I: Ancient Egyptian Numeration System
• Part II: Egyptian Method of Decomposing
Fractions to Unit Fractions
• Part III: Partial Fractions
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Part I: Ancient Egyptian Numeration
System
• Activity #1 on Egyptian Numeration System
• Video on Egyptian Numeration System
• Activity #2 Writing Numbers from Arabic
Numerals to Egyptian Numerals and vice-versa
• challenge question, “In our number system we
just add a zero at the end of a number if we
want to multiply by 10. How would you
multiply by 10 using hieroglyphics?”
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Part II: Egyptian Method of
Decomposing Fractions to Unit
Fractions
• Introduction to Egyptian fractions by showing
the parts of the Eye of Horus and its
corresponding unit fraction.
• Activity 3 on Egyptian Fractions
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Part III: Partial Fractions
• Introduction of partial fraction decomposition
• Worksheet on Partial Fraction Decomposition
Case 1: Distinct Linear Factors
• Students reflect and ponder on the question,
“What will happen if our denominator has a
repeated linear factor?”
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
RESULTS AND DISCUSSION
(Productive Pedagogy)
Intellectual Quality
Connectedness
Supportive Classroom Environment
Recognition of Difference
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Intellectual Quality
• Series of activities were employed to assess
the students’ understanding of the topic
through pictures related to Egypt.
• Teacher-student interaction
• Students had much more rapport with the
task given to them than with the teacher.
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Connectedness
• Students are engaged with real, practical or hypothetical
problems which connect to the world beyond the
classroom, which are not restricted by subject boundaries,
and which are linked to their prior knowledge.
• It was also observed that even those students who were
not really good in mathematics were engaged on the tasks
given while the students expressed the same feelings in
Ancient Egyptian Mathematics and its numerical system.
• The teacher made the students feel the significance of
dividing it in such manner by making them experience how
Egyptians did it.
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Supportive Classroom Environment
• Teacher's interaction with the students can
create an environment of respect and rapport
in their classrooms.
• Student-centered activities
• Social support was very evident in the
implementation of the lesson.
• Students were very attentive during the class
discussions and were very willing to do and
finished the assigned tasks given to them.
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Supportive Classroom Environment
The observers commended the following:
(1) The activities were good and friendly to those
who were not so numerically inclined.
(2) It was clear to students what they would do in
class.
(3) Students were well-monitored during each
activity, that is why they felt at ease in the class.
(4) The teacher allowed the students to participate
in the discussion.
(5) The lesson was delivered well.
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Supportive Classroom Environment
The observers noted the following:
(1) The answers in the examples should have been
checked if they really add up to the original fraction.
(2) The teacher could have given opportunities for the
students to process information and to eliminate the
tendency of spoon-feeding.
(3) In order for the students to provide sound and
reasonable conclusions, the teacher could have
thrown questions and process the scenario.
(4) The teacher could have given opportunities for the
students to be recognized when they want to provide
responses to the teacher’s questions.
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Recognition of Difference
• The researchers designed all class activities wherein
students would have the opportunities to collaborate with
fellow learners.
• The class was divided into 4 groups named after the
Egyptian gods: Thoth, Horus, Osiris, and Isis
• The students have had no negative reaction about the
name assigned to their individual group.
• During the course of the activity, the abundance of the
integration of historical accounts was used by the teacher
as a springboard for each of the planned activities.
• Both the observers and the students agreed that the
integration of the history of ancient Egyptian helped them
maintain the motivation on the duration of the lesson.
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
CONCLUDING REMARKS
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
• Students enjoyed the lesson according to their
responses in their surveys.
• They were also able to connect various mathematical
concepts such as addition of fractions, counting and
dissimilar fractions in Egyptian mathematics and read
numbers through Egyptian symbols.
• The students were able to participate during the series
of activities and discussions from the teacher.
• The teaching strategies were progressive and learnerfriendly.
Integrating Ancient Egyptian Mathematics in Teaching Partial Fractions through Lesson Study
Thank you!