Volume 03 Issue 05-2023
108
International Journal of Pedagogics
(ISSN
–
2771-2281)
VOLUME
03
ISSUE
05
Pages:
108-112
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
6.
676
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
ABSTRACT
In the article we will consider the problem relevant in higher educational institutions, namely: what stages should
constitute a mathematics lesson, also, at each stage, what methods should be used in order to develop students'
cognitive activity.
KEYWORDS
Phases (or parts), introduce, investigate, explore, wrap-up, learning task, intriguing problems, math concepts, planned
discussions and activities, ways of learning, problematic question, conjectures, misconceptions, alternative
explanations, conclusions, organize information, mathematical language, observing, classifying, communicating,
measuring, predicting, interpreting, organize information, develop, extend, connect, instructional step.
INTRODUCTION
When teachers nurture a safe learning community
within their classrooms, students respect each other’s
ideas, are patient with one another, recognize there
can be multiple perspectives and ways of learning, and
recognize the value of individual contributions to
group learning [1]. With their anxiety lowered,
students are physiologically more able to accept new
challenges and grapple with new concepts and
problems. Notwithstanding high education, in
particular math
’ community has not reached
consensus about what to call them, it is common
practice among research-based math curricula to
organize lessons into three phases (or parts).
During the first phase, often called “introduce”, the
teacher encourages students to draw on their prior
knowledge in order to engage with a new concept. In
phase two, “investigate” or “explore,” students work
with the new concept in the form of a meaningful
problem [2]. During the third phase of a mathematics
lesson, “summarize” or “wrap
-
up,” students and
Research Article
METHODS THAT DEVELOP THE DIDACTIC STRUCTURE OF STUDENTS'
COGNITIVE ACTIVITY IN THREE STAGES OF A MATH LESSON
Submission Date:
May 17, 2023,
Accepted Date:
May 22, 2023,
Published Date:
May 27, 2023
Crossref doi:
https://doi.org/10.37547/ijp/Volume03Issue05-22
Yunusova Gulnoza Abduxalikovna
Phd, Associate Professor, Department Of Natural Sciences Of The Academy Of The Armed Forces Of The
Republic Of Uzbekistan
Journal
Website:
https://theusajournals.
com/index.php/ijp
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Volume 03 Issue 05-2023
109
International Journal of Pedagogics
(ISSN
–
2771-2281)
VOLUME
03
ISSUE
05
Pages:
108-112
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
6.
676
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
teachers draw conclusions and make connections to
related concepts.
MATERIALS AND METHODS
According to John Carr, Catherine Carroll, Sarah
Cremer, Mardi Gale, Rachel Lagunof, and Ursula
Sexton in this article, we use introduce, investigate,
and summarize to label the three phases, as
reflected in Figure 1.1.
Introduce
Assess
Summarize Investigate
Figure 1.1. THREE PHASES OF MATHEMATICS INSTRUCTIONS
Note that student assessment is continuous
throughout the three phases because teachers use
feedback from assessment to adjust instruction during
all phases [3]. Each of the three phases is described
below, followed by an except of a teacher’s vision for
implementing that phase in the classroom.
RESULT AND DISCUSSION
Introduce. The learning process begins as the teacher
guides students to make connections between the
learning task at hand and their past academic,
personal, and cultural experiences. The goal is to
engage students in learning by sparking their curiosity,
posing intriguing problems, or asking thought-
provoking questions. This phase also offers the teacher
opportunities to identify students’ preconceptions and
misconceptions about a mathematical concept. When
misconceptions arise, they are simply acknowledged
along with other brainstorming ideas, but the teacher
mentally notes these misunderstandings to ensure
that they are explicitly addressed at the proper time
[1].
As part of this phase, it can also be useful for a teacher
to make explicit the goal math concepts of theme and
that are the focus of the lesson. For example,
Volume 03 Issue 05-2023
110
International Journal of Pedagogics
(ISSN
–
2771-2281)
VOLUME
03
ISSUE
05
Pages:
108-112
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
6.
676
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
teacher presents these objectives to students orally
and in writing. Doing so makes it crystal clear to
students how the planned discussions and activities.
When the teacher makes learning objectives explicit, it
helps all students focus on the “bull’s eye” from the
start of the lesson; and it sets the basis for students to
reflect on how well they achieved those objectives at
the end of the lesson. The teacher plans a lesson that
targets those specific content and language objectives,
and reflects after the lesson on how well the
instructional strategies and learning activities stayed
on course and met the objectives.
In my class . . . I begin my lesson with an intriguing idea,
image, or problematic question (for example like
‘branch storm’) to engage students. I pose questions
about what my students (nowadays cadets) already
know, make conjectures about how to solve a
problem, and encourage them to pose questions about
what they want to learn. This alerts me to what my
cadets already know, their misconceptions, and areas
of potential confusion [4].
Investigate. The teacher guides students as they
investigate a mathematical task, work toward a
common understanding of specific concepts, and
acquire problem-solving and computational skills. The
teacher designs activities that encourage students to
construct new knowledge or skills, propose
preliminary ways of thinking about a problem,
“puzzle” through problems, and try alternatives to get
a solution. As students engage with the mathematics,
the teacher encourages them to demonstrate or
explain their conceptual understanding of the problem
and the process skills they used to arrive at their
conclusion. Students debate alternative explanations
for their conclusions and use new facts to correct their
prior misconceptions. As appropriate, the teacher
directs students’ attention back to helpful points from
the introduce phase of instruction. Students are
guided to organize information supporting their ideas
or conclusions into evidence-based statements, using
mathematical language.
In my class . . . Rather than telling my cadets the
concepts I want them to learn, I expect them to think
critically about the concepts by experimenting,
investigating, observing, classifying, communicating,
measuring, predicting, and interpreting. This active
engagement arouses their curiosity and leads them to
discover new ideas or reconsider their earlier thinking.
I guide cadets to explain their thinking by asking
questions and facilitating peer discussions, by giving
them time to think, and I facilitate active discussions
to correct misconceptions. I provide time to question
and justify answers. I do not just answer questions that
students pose, nor do I simply decide for them which
answers are right or wrong.
Summarize. The summarizing phase involves more
than just revisiting what has been learned. During this
phase, the teacher engages students in activities and
discussions that challenge and extend their conceptual
understanding and problem-solving skills. Students
apply what they have learned to new mathematical
tasks and experiences to develop, extend, connect,
and deepen their understanding of the concepts [5].
In my class . . . At the end of an instructional step, I help
cadets compare, contrast, combine, synthesize,
generalize, and make inferences by asking them to
solve a problem or perform a task that introduces a
somewhat different context from those they have just
experienced. I want cadets to be able to apply new
knowledge, make connections, and extend ideas.
Assess. Throughout the three phases of inquiry-based
mathematics instruction, the teacher assesses
Volume 03 Issue 05-2023
111
International Journal of Pedagogics
(ISSN
–
2771-2281)
VOLUME
03
ISSUE
05
Pages:
108-112
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
6.
676
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
students’ progress and asks students to evaluate
themselves. Feedback may come from quick, on-the-
spot checks for understanding (e.g., expressed with
hand gestures, white boards), quizzes, student
discussions, journals, or other techniques [6]. The
teacher uses the feedback to reflect on how effective
a class was, and to make mid-lesson adjustments to
better meet students’ needs and interests. Students
use the feedback to reflect on what they understand,
what they still need to learn, and what they want to
learn next [7].
In my class . . . I test cadets on more than just factual
knowledge; during an assessment, I challenge cadets
to construct ideas and explanations, just as I do during
class instruction.
I want assessments to reflect both my
objectives and the content standards. As a facilitator,
the teacher nurtures creative thinking, problem
solving, interaction, communication, and discovery.
Finally, as a guide, the teacher helps to bridge language
gaps and foster individuality, collaboration, and
personal growth. The teacher moves flexibly into and
out of these various roles, as appropriate for each
lesson [8].
CONCLUSION
One of the promising directions of monitoring the
quality of knowledge as a condition of personality-
oriented continuous education can be active methods
of education, the analysis of which showed that the
cognitive interests of students manifested in a
particular subject area are proportional to the results
in the relevant academic disciplines [9], and at the
same time revealed that the formed cognitive interest
regardless of, in which subject area it is formed, has a
positive impact on the overall effectiveness of training,
providing-higher level of both natural-mathematical
and humanitarian education; and also to increase the
effectiveness of cognitive activity of students in
subjects not related to the sphere of their professional
interests, which ensures the effectiveness of the
organization of personality-oriented continuing
education [7,9].
REFERENCES
1.
Hawkins, B. (2005). Mathematics education for
second language students in the mainstream
classroom. In P.A. Richard-Amato, & M.A.
Snow, (Eds.), Academic success for English
language learners, (p. 380). White Plains, NY:
Pearson Education, Inc.
2.
Moschkovich, J. (1999). Supporting the
participation of English language learners in
mathematical discussions. For the Learning of
Mathematics, 19 (1), 11
–
19.
3.
G. A. Yunusova. Monitoring the results of
students’ collaborative learning.
- Science and
innovation.
–
V2 Issue 1, UIF-2022: 8.2 ISSN:
2181-3337. P.294-297.
4.
G. A. Yunusova. Monitoring the quality of
knowledge in the person-oriented education
system. - International Conference On
Teaching Education And New Learning
Technologies 2023/2. ISSN: 2181-3515. 26
January, 2023 Year. P. 641-643.
5.
Д.
И.
Юнусова.
Применение
информационных технологий в подготовке
педагогических кадров.
-
Информатика и
образование, 51
-
52, 2008, №11.
6.
Ш.
А.
Пазилова.
Усовершенствование
преподавания
дисциплины
основы
электротехники и электроники. –
Educational
Research in Universal Sciences 1 (6), 251-255,
2022.
7.
Д. И. Юнусова. Инновации в предметно
-
методической
подготовке
будущих
Volume 03 Issue 05-2023
112
International Journal of Pedagogics
(ISSN
–
2771-2281)
VOLUME
03
ISSUE
05
Pages:
108-112
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
6.
676
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
учителей
математики.
-
Сибирский
педагогический журнал, 316
-
323, 2008, №6.
8.
Sh. Pazilova. The relevance of the application
of the mixed form of education in higher
military educational institutions.
–
Science and
innovation 2 (1), 95-97, 2023.
9.
http://www.wested.org/online
pubs/CC-
0901Carr Math_chapter1.pdf
