The teaching cycle in mathematics

Example: Teacher Gina thought it is best to apply constructivist

approach to help her students learn techniques in multiplying
whole numbers. She planned a lesson that incorporates the
problem solving strategy.

3. Implement Plan

This is the stage where you conduct the learning activities that you
have prepared during the planning stage. A word of advice: even
though you have carefully and delicately planned for the lesson, you
must be flexible with the possible changes that you need to
accommodate.

Example: The class went on smoothly. The activities that teacher Gina
prepared were successfully done by her students.

1. Identify objects
What knowledge and/or skills do the students need to learn? 4. Check for understanding
You must be guided by the a content standards, performance
standards, and the learning competencies that are found in Teaching is a understandinghplementation of the lesson plan, you
the curriculum guide. must every now and then check whether the students have
understood what you have covered so far. Facial reactions and verbal
Example: Teacher Gina identified "multiplication of whole cues help in assessing whether or not the students can move on to
numbers up to two digits" as the goal of her lesson. another concept or skill. If not, you might need to give a more
elaborate explanation, more examples, or whatever you think is
2. Plan Instruction needed based on the student's reaction.
What strategies must be implemented for the students to achieve
the objectives targeted in the previous stage? In planning
instruction, it is important that you have mastered the content of Example: To make sure that her students understood the lesson
the lesson that you are about to teach. It is also beneficial to be teacher Gina gave a three-item exercise as an exit pass.
familiar with your students- what they know, how they learn, etc.
 Example: Teacher Gina Teacher Gina later on gave a multiplication quiz.
Ninety percent of the students passed. She planned to give remedial
5. Reflect on Teaching exercises to those who failed.
You must evaluate every teaching period that you finished. Were the
objectives achieve? Were the implemented strategies effective? How
can the instructions be improved? Your answers to the last questions
will give you insights on how to improve instruction the next time you
teach the same lesson. However, if your answer in the first question is
no, i.e., the objectives were not met, then you need to plan again.
What do you need to do differently in order to achieve the objectives?

Example: Based on the exit pass, Teacher Gina found out that many
students have difficulty multiplying numbers that involve the digit 8.
So, she decided to do a find- your-error activity the next day for the
students to realize their mistakes. She also planned to give a short
drill on skip counting by 8.

6. Assessing learning and reflect on the results

This stage gives you a complete measure of what the students have
learned. In math, this is usually through a paper and pencil examination.
However some authentic assessments may also be implemented. Take
note that this stage does not end in assessing learning. You need to reflect
on the results, what can you learn about student learning and teaching
practice based on the results?

After assessment and reflection, you will once again identify the next
learning goals and so the cycle continues.
Constructivist theory in teaching
mathematics in the primary grades
Constructivist Learning Theory
• States that learning is an active process of creating meaning
from different experiences. In other words, students learn
best by trying to make sense of something on their own with
a teacher as a guide.
What is constructivism?
• Is a learning model that teaches through hands-on
experiences rather than lectures.
• Was conceptualized by education theorist Jean Piaget. He
believes that “young children learn by doing, constructing
knowledge from experiences rather than from adults telling
them about their world.”
Things to Consider in Planning Instruction in 2. Objectives

Mathematics in the Primary Grades. Before you begin planning, you need to know what specific knowledge
and skills you want your students to develop during the lesson or unit.
- In education, planning refers to the designing and Teachers often focus too much on knowledge, forgetting about developing
preparation of learning activities for students. In lesson skills which in the long term are more important than knowing mere facts.
planning, the teachers thoughtfully contemplate about the So, in planning your instruction, always consider both knowledge and
lesson objectives, the activities that will meet these skills.
objectives, the sequence of those activities, the materials
needed, how long each activity might take, how the class
would be managed during those activities, and the 3. Students
evaluation method to assess how far the objectives were
met. This lesson enumerates the things to consider in Get to know your students-where they came from, what their Interests
planning instruction in mathematics in the primary grades. are, what they already know, their learning style, attention span, special
needs, etc. These will all help you determine your students' needs.
Remember that you need to prepare your lessons with all your students in
five important elements in lesson planning that you need to consider- mind and that your main goal should be to meet their needs and offer
content, objectives, students, learning environment, and availability of them enabling environments to learn their preferred way.
resources.

1. Content
4. Learning environment
Research the subject matter that you will be teaching. You should consult
the curriculum and teaching guides published by DepEd. Aside from Aside from the physical environment where the learning takes place, it is
books, you can also visit websites which will give you information relevant also important to consider the social and emotional learning environment
to your subject area. You should master the contents of your lesson of the class. You need to make sure that you promote a positive
before you teach it. Remember, you cannot give what you do not have. environment where students are motivated and are supportive of each
Moreover, you would not want to teach wrong contents to the students. It other's growth. The students must feel safe to express their thinking,
is easier to learn than to unlearn; it is difficult to take back wrong contents without fear of being embarrassed because of mistakes or different views.
that have already been taught. You have a big responsibility as a teacher- Most importantly, you must create an atmosphere where students are
master your content! open to learning through the activities you prepared and interactions with
their classmates.
5. Availability of resources Discussion
Take into consideration the instructional materials that you will be The lesson proceeds with the processing of the activity. In this part, the
needing before you write your lesson plan. Is a blackboard available? If students, as facilitated by the teacher, talks about their experiences
not, can you improvise? Are there specific manipulatives that you need? during the activity. Here, the questioning skills of the teacher is important
Where can you get them? Can you make them instead? Do you need because he/she must be able to direct the discussion toward the targeted
technology resources? Have you checked whether your devices are lesson
compatible with what are available in school? These are some of the
questions that you can reflect on.
Input
In a traditional classroom, the input is where the teacher lectures.
However, in a constructivist classroom, this is the part where the students
would share the concepts that they learned based on the activity and the
dicussion. Nevertheless, no matter which learning theory is applied in the
Instructional planning models for mathematics in lesson, this is the part where the concepts are clearly established.
primary Deepening
There are many instructional planning models that mathematics Here the teacher asks questions that will engage the students to critical
educators have constructed, but the two most widely used in the and creative thinking. Nonroutine mathematical problems or real-life
Philippines are the ADIDAS and the Five Es models. ADIDAS stands for word problems may be given. The purpose is to give the students the
Activity, Discussion, input, Deepening, Activity, and Summary opportunity to deepen their understanding of the concepts that they have
just learned

Activity Activity

The lesson begins with an activity that will later facilitate a meaningful In mathematics, this is the part where the students verify what they have
discussion about the topic of the session, in other words, the activity just learned by solving mathematical problems. Depending on the heed,
introduces the topic to the students. This activity must be motivating and the students may be engaged in guided practice and/or individual
engaging to catch the attention of the students practice. Sometimes, the teacher facilitates games in this part of the
lesson
Synthesis
The last part of the ADIDAS model is the Synthesis. Here the students are Explain
given the opportunity to express what they have learned by verbally
Here the students explain what they have experienced in Explore. The role
giving a summary of what transpired in class and what they have learned.
of the teacher is to facilitate the discussion that should lead to students
The students may also be given a short assessment to give the teacher
seeing patterns that will help them to describe the new concept in their
feedback on what they have learned
own words

Elaborate
Another commonly used instructional planning model in our country is
The Elaborate part of the lesson allows students to expand their
the Five Es. The Five Es are Engage, Explore, Explain, Elaborate, and
understanding of the concept by applying the concept that they have
Evaluate
learned in solving mathematical problems

Evaluate
Engage
The last part of the Five Es model, Evaluate, lets the teacher and the
This part activates the students' prior knowledge and engages them into students evaluate their learning. Though giving short exercises are usually
new concepts by doing short activities. The aim of this part is to arouse the mode of evaluation, the teacher can be creative by implementing
the students curiosity other evaluation activities

Explore
In this part, the students are exposed to different experiences that will
facilitate the discovery of new concepts. Explore may involve observation
exercises. simulations, or manipulations of instructional materials. The
goal here is for the students to discover something new
INSTRUCTIONAL STRATEGIES FOR MATHEMATICS 7. Technology Use: Using computers, tablets, or interactive
whiteboards with math games or apps. These tools can
IN THE PRIMARY GRADES make learning more engaging and give students different
ways to understand math concepts.
8. Differentiated Instruction: Adapting lessons to fit students'
1. Direct Teaching: The teacher explains math concepts clearly,
needs. Some students may need easier tasks, while others
step by step, showing students how to solve problems. This
need more challenging work. This way, everyone can learn
helps students understand the basics before they try on
at their own pace.
their own.
9. Frequent Check-Ins (Formative Assessment): The teacher
2. Hands-On Activities (Manipulatives): Using objects like
regularly checks how well students are understanding the
blocks, beads, or counters to help students see and touch
lessons through quizzes, questions, or class activities. This
what they’re learning. This makes math more concrete and
helps adjust teaching to focus on areas where students need
easier to understand, especially for younger kids.
more help.
3. Guided and Independent Practice: After teaching a concept,
10. Math Journals: Students write about how they solved a
the teacher helps students practice solving problems
problem or explain what they learned. Writing helps them
together. Then, students work independently to make sure
think about their process and understand the math better.
they can do it on their own.
11. Class Discussions (Math Talks): Students discuss math
4. Real-Life Problem Solving: Presenting problems that relate
problems together and explain their thinking. This helps
to everyday situations, like shopping or measuring
build their confidence and improves their problem-solving
ingredients. This helps students see why math is useful and
skills.
makes learning more interesting.
12. Inquiry-Based Learning: Instead of giving all the answers,
5. Small Group Work (Cooperative Learning): Students work in
the teacher asks questions that make students think and
pairs or small groups to solve problems. They can talk about
explore math ideas on their own. This encourages curiosity
their ideas, help each other, and learn to work together.
and deeper understanding.
6. Math Centers: Setting up different stations in the classroom
where students can practice math skills through games,
puzzles, or hands-on activities. This keeps learning fun and
interactive